Choose the correct answer.
If $\text{f(x)}=\cos^2\text{x}+\sec^2\text{x},$ then:
If $\text{f(x)}=\cos^2\text{x}+\sec^2\text{x},$ then:
- A$\text{f(x)}<1$
- B$\text{f(x)}=1$
- C$2<\text{f(x)}<1$
- D$\text{f(x)}\geq2$
Question types
Trigonometric Functions question types
528 questions across 9 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
528
Questions
9
Question groups
5
Question types
01
M.C.Q (1 Marks)
184 Q→02True False[1 Marks ]
8 Q→03Fill In The Blanks[1 Marks ]
8 Q→041 Marks Question
31 Q→052 Marks Questions
47 Q→063 Marks Question
12 Q→075 Marks Questions
231 Q→08Assertion (A) & Reason (B) MCQ
5 Q→09Case study (4 Marks)
2 Q→Sample Questions
Trigonometric Functions questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $\text{cosec x}+\cot \text{x}=\frac{11}{2},$ then $\tan\text{x}$ is equal to:
- A$\frac{21}{22}$
- B$\frac{15}{16}$
- C$\frac{44}{117}$
- D$\frac{117}{44}$
The value of $\frac{\sin5\alpha-\sin\beta}{\cos5\alpha+2\cos4\alpha+\cos3\alpha}$ is:
- A$\cot\frac{\alpha}{2}$
- B$\cot\alpha$
- C$\tan\frac{\alpha}{2}$
- DNone of these
If in $\text{a}\triangle\text{ABC},\tan\text{B}+\tan\text{C}=6,$ then $\cot\text{A}\cot\text{B}\cot\text{C}=$
- A$6$
- B$1$
- C$\frac16$
- DNone of these
$\text{If}\ \sin\alpha+\sin\beta=\text{a}\text{ and }\cos\alpha-\cos\beta=\text{b},\ \text{than }\tan\frac{\alpha-\beta}{2}=$
- A$-\frac{\text{a}}{\text{b}}$
- B$-\frac{\text{b}}{\text{a}}$
- C$\sqrt{\text{a}^2+\text{b}^2}$
- DNone of these
State True or False for the following statement:
$\sin10^\circ$ is greater than $\cos10^\circ.$
View full solution →$\sin10^\circ$ is greater than $\cos10^\circ.$
State True or False for the following statement:
One value of $\theta$ which satisfies the equation $\sin^4\theta-2\sin^2\theta-1$ lies between 0 and $2\pi.$
View full solution →One value of $\theta$ which satisfies the equation $\sin^4\theta-2\sin^2\theta-1$ lies between 0 and $2\pi.$
State True or False for the following statement:
If $\tan\text{A}=\frac{1-\cos\text{B}}{\sin\text{B}},$ then $\tan2\text{A}=\tan\text{B}$
View full solution →If $\tan\text{A}=\frac{1-\cos\text{B}}{\sin\text{B}},$ then $\tan2\text{A}=\tan\text{B}$
State True or False for the following statement:
If $\tan(\pi\cos\theta)=\cot(\pi\sin\theta),$ then $\cos\Big(\theta-\frac{\pi}{4}\Big)=\pm\frac{1}{2\sqrt{2}}$
View full solution →If $\tan(\pi\cos\theta)=\cot(\pi\sin\theta),$ then $\cos\Big(\theta-\frac{\pi}{4}\Big)=\pm\frac{1}{2\sqrt{2}}$
State True or False for the following statement:
If $\text{cosec x }=1+\cot\text{x}$ then $\text{x}=2\text{n}\pi,2\text{n}\pi+\frac{\pi}{2}$
View full solution →If $\text{cosec x }=1+\cot\text{x}$ then $\text{x}=2\text{n}\pi,2\text{n}\pi+\frac{\pi}{2}$
Fill in the blank.
In a triangle ABC with $\angle\text{C}=90^\circ$ the equation whose roots are tan A and tan B is _______.
[Hint: $\text{A + B}=90^\circ\Rightarrow\tan\text{A}\tan\text{B}=1$ and $\tan\text{A}+\tan\text{B}=\frac{2}{\sin2\text{A}}$ ]
View full solution →In a triangle ABC with $\angle\text{C}=90^\circ$ the equation whose roots are tan A and tan B is _______.
[Hint: $\text{A + B}=90^\circ\Rightarrow\tan\text{A}\tan\text{B}=1$ and $\tan\text{A}+\tan\text{B}=\frac{2}{\sin2\text{A}}$ ]
Fill in the blank.
If $\sin\text{x}+\cos\text{x}=\text{a},$ then,
View full solution →If $\sin\text{x}+\cos\text{x}=\text{a},$ then,
- $\sin^6\text{x}+\cos^6\text{x}=$ _______
- $|\sin\text{x}-\cos\text{x}|=$ _______.
Fill in the blank.
Given x > 0, the values of $\text{f(x)}=-3\cos\sqrt{3+\text{x + x}^2}$ lie in the interval _______.
View full solution →Given x > 0, the values of $\text{f(x)}=-3\cos\sqrt{3+\text{x + x}^2}$ lie in the interval _______.
Fill in the blank.
If $\tan\text{A}=\frac{1-\cos\text{B}}{\sin\text{B}},$ then $\tan2\text{A}=$ _______.
View full solution →If $\tan\text{A}=\frac{1-\cos\text{B}}{\sin\text{B}},$ then $\tan2\text{A}=$ _______.
Fill in the blank.
The value of $\frac{\sin50^\circ}{\sin130^\circ}$ is _______.
View full solution →The value of $\frac{\sin50^\circ}{\sin130^\circ}$ is _______.
Prove that: $\frac { \cos ( \pi + x ) \cos ( - x ) } { \sin ( \pi - x ) \cos \left( \frac { \pi } { 2 } + x \right) } = \cot ^ { 2 } x$ .
View full solution →Prove that: $\frac { \tan \left( \frac { \pi } { 4 } + x \right) } { \tan \left( \frac { \pi } { 4 } - x \right) } = \left( \frac { 1 + \tan x } { 1 - \tan x } \right) ^ { 2 }$
View full solution →Prove that $\cos \left( {\frac{\pi }{4} - x} \right)\cos \left( {\frac{\pi }{4} - y} \right) - \sin \left( {\frac{\pi }{4} - x} \right)$$\sin \left( {\frac{\pi }{4} - y} \right) = \sin (x + y)$
View full solution →Prove that cot x cot2x - cot2x cot3x - cot3x cotx = 1
Prove that: $\frac{\sin x+\sin 3 x}{\cos x+\cos 3 x}=\tan 2 x$
View full solution →Prove that : $\frac { ( \sin 7 x + \sin 5 x ) + ( \sin 9 x + \sin 3 x ) } { ( \cos 7 x + \cos 5 x ) + ( \cos 9 x + \cos 3 x ) } = \tan 6 x$
View full solution →Prove that : sin x + sin 3x + sin 5x + sin 7x = 4 cos x cos 2x sin 4x
Prove that: $(\cos x-\cos y)^{2}+(\sin x-\sin y)^{2}=4 \sin ^{2} \frac{x-y}{2}$
View full solution →Prove that : (cos x + cos y)2 + (sin x - sin y)2$ = 4{\cos ^2}\frac{{x + y}}{2}$
View full solution →Prove that : (sin 3x + sin x) sin x + (cos 3x - cos x) cos x = 0
Find sin $\frac{x}{2},\cos \frac{x}{2}$ and $\tan \frac{x}{2}$ in the $\cos\;x\;=-\frac13$, x in quadrant III.
View full solution →Find sin $\frac{x}{2},\cos \frac{x}{2}$ and $\tan \frac{x}{2}$ in the $\tan x = - \frac{4}{3}$, x in quadrant II.
View full solution →Prove that : sin 3x + sin 2x - sin x $ = 4\sin \;x\cos \frac{x}{2}\cos \frac{{3x}}{2}$
View full solution →Find sin $\frac{x}{2},\cos \frac{x}{2}$ and $\tan \frac{x}{2}$ in the $\sin x = \frac{1}{4}$, x in quadrant II.
View full solution →Prove that: cos 6x = 32 cos6 x – 48 cos4 x + 18 cos2 x – 1
Prove that:
$\sin3\text{x}+\sin2\text{x}-\sin\text{x}=4\sin\text{x}\cos\Big(\frac{\text{x}}{2}\Big)\cos\Big(\frac{3\text{x}}{2}\Big)$
View full solution →$\sin3\text{x}+\sin2\text{x}-\sin\text{x}=4\sin\text{x}\cos\Big(\frac{\text{x}}{2}\Big)\cos\Big(\frac{3\text{x}}{2}\Big)$
Find the general solution for each of the following equations:
$\sec^22\text{x}=1-\tan2\text{x}$
View full solution →$\sec^22\text{x}=1-\tan2\text{x}$
Find the general solution for each of the following equations:
$\sin2\text{x}+\cos\text{x}=0$
View full solution →$\sin2\text{x}+\cos\text{x}=0$
Prove that:
$(\cos\text{x}+\cos\text{y})^2+(\sin\text{x}-\sin\text{y})^2=4\cos^2\frac{\text{x}+\text{y}}{2}$
View full solution →$(\cos\text{x}+\cos\text{y})^2+(\sin\text{x}-\sin\text{y})^2=4\cos^2\frac{\text{x}+\text{y}}{2}$
Prove that:
$\frac{(\sin7\text{x}+\sin5\text{x})+(\sin9\text{x}+\sin3\text{x})}{(\cos7\text{x}+\cos5\text{x})(\cos9\text{x}+\cos3\text{x})}=\tan6\text{x}$
View full solution →$\frac{(\sin7\text{x}+\sin5\text{x})+(\sin9\text{x}+\sin3\text{x})}{(\cos7\text{x}+\cos5\text{x})(\cos9\text{x}+\cos3\text{x})}=\tan6\text{x}$
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
If $\text{A} + \text{B} + \text{C} = 180^\circ$, then
Assertion: $\cos^{2}\frac{\text{A}}{2}+\cos^{2}\frac{\text{B}}{2}-\cos^{2}\frac{\text{C}}{2}$
$=2\cos\frac{\text{A}}{2}\cos\frac{\text{B}}{2}\sin\frac{\text{C}}{2}.$
Reason: $\cos\text{C}+\cos\text{D}=2\cos\Big(\frac{\text{C}+\text{D}}{2}\Big)\cos\Big(\frac{\text{C}+\text{D}}{2}\Big).$
View full solution →If $\text{A} + \text{B} + \text{C} = 180^\circ$, then
Assertion: $\cos^{2}\frac{\text{A}}{2}+\cos^{2}\frac{\text{B}}{2}-\cos^{2}\frac{\text{C}}{2}$
$=2\cos\frac{\text{A}}{2}\cos\frac{\text{B}}{2}\sin\frac{\text{C}}{2}.$
Reason: $\cos\text{C}+\cos\text{D}=2\cos\Big(\frac{\text{C}+\text{D}}{2}\Big)\cos\Big(\frac{\text{C}+\text{D}}{2}\Big).$
- Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- Assertion is correct statement but Reason is wrong statement.
- Assertion is wrong statement but Reason is correct statement.
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Let $\sec\theta+\tan\theta=\text{m},$ where 0 < m < 1.
Assertion: $\sec\theta=\frac{\text{m}^{2}+1}{2\text{m}}$ and $\sin\theta=\frac{\text{m}^{2}-1}{\text{m}^{2}+1}.$
Reason: $\theta$ lies in the third quadrant.
View full solution →Let $\sec\theta+\tan\theta=\text{m},$ where 0 < m < 1.
Assertion: $\sec\theta=\frac{\text{m}^{2}+1}{2\text{m}}$ and $\sin\theta=\frac{\text{m}^{2}-1}{\text{m}^{2}+1}.$
Reason: $\theta$ lies in the third quadrant.
- Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- Assertion is correct statement but Reason is wrong statement.
- Assertion is wrong statement but Reason is correct statement.
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Let $\alpha$ be a real number lying between 0 and $\frac{\pi}{2}$ and n be a positive integer.
Assertion: $\tan\alpha+2\tan2\alpha+2^{2}\tan2^{2}\alpha+...+2^{\text{n-1}}\tan2^{\text{n}-1}\alpha+2^{\text{n}}\cot2^{\text{n}}\alpha=\cot\alpha.$
Reason: $\cot\alpha-\tan\alpha=2\cot2\alpha.$
View full solution →Let $\alpha$ be a real number lying between 0 and $\frac{\pi}{2}$ and n be a positive integer.
Assertion: $\tan\alpha+2\tan2\alpha+2^{2}\tan2^{2}\alpha+...+2^{\text{n-1}}\tan2^{\text{n}-1}\alpha+2^{\text{n}}\cot2^{\text{n}}\alpha=\cot\alpha.$
Reason: $\cot\alpha-\tan\alpha=2\cot2\alpha.$
- Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- Assertion is correct statement but Reason is wrong statement.
- Assertion is wrong statement but Reason is correct statement.
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The value of $\sin(-690^\circ)\cos(-300^\circ)+\cos(-750^\circ)\sin(-240^\circ)=1.$
Reason: The values of $\sin$ and $\cos$ is negative in third and fourth quadrant respectively.
View full solution →Assertion: The value of $\sin(-690^\circ)\cos(-300^\circ)+\cos(-750^\circ)\sin(-240^\circ)=1.$
Reason: The values of $\sin$ and $\cos$ is negative in third and fourth quadrant respectively.
- Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- Assertion is correct statement but Reason is wrong statement.
- Assertion is wrong statement but Reason is correct statement.
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The value of $\theta=\frac{\pi}{3}$ or $\frac{2\pi}{3},$ when $\theta$ lies between $(0,2\pi)$ and $\sin^{2}\theta=\frac{3}{4}.$
Reason: $\sin\theta$ is positive in the first and second quadrant.
View full solution →Assertion: The value of $\theta=\frac{\pi}{3}$ or $\frac{2\pi}{3},$ when $\theta$ lies between $(0,2\pi)$ and $\sin^{2}\theta=\frac{3}{4}.$
Reason: $\sin\theta$ is positive in the first and second quadrant.
- Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- Assertion is correct statement but Reason is wrong statement.
- Assertion is wrong statement but Reason is correct statement.
Rajiv constructs two right angled triangles in the fourth quadrant in such a way that the measure of triangle gives $\cos A=\frac{4}{5}$ and $\cos B=\frac{12}{13}$, where $\frac{3 \pi}{2} < A$ and $B > 2 \pi$.
Based on the above information, answer the following questions.
(i) Find the value of $\cos (A+B)$
(ii) Find the value of $\sin (A-B)$
(iii) Find the value of $\tan (\mathbf{A}+\mathbf{B})$
View full solution →Based on the above information, answer the following questions.
(i) Find the value of $\cos (A+B)$
(ii) Find the value of $\sin (A-B)$
(iii) Find the value of $\tan (\mathbf{A}+\mathbf{B})$
In a class test of class XI, a teacher asked to students to consider $\mathbf{A}+\mathbf{B}=\frac{\pi}{4}$, where $\mathbf{A}$ and $\mathbf{B}$ are acute angles.
Based on the above information, answer the following questions.
(i) Find the value of $(1+\tan A)(1+\tan B)$ ?
(ii) Find the value of $(\cot \mathbf{A}-1)(\cot \mathbf{B}-1)$ ?
(iii) Find the value of
$
\sin (A+B)-\cos (A+B)+\tan (A+B) .
$
View full solution →Based on the above information, answer the following questions.
(i) Find the value of $(1+\tan A)(1+\tan B)$ ?
(ii) Find the value of $(\cot \mathbf{A}-1)(\cot \mathbf{B}-1)$ ?
(iii) Find the value of
$
\sin (A+B)-\cos (A+B)+\tan (A+B) .
$
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