The value of $\tan45^\circ\times\cot45^\circ$ is :
- A$0$
- ✓$1$
- C$2$
- D$\frac{1}{2}$
Answer: B.
View full solution →Question types
Introduction of Trigonometry question types
362 questions across 9 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
362
Questions
9
Question groups
5
Question types
01
M.C.Q (1 Marks)
226 Q→02Assertion (A) & Reason (B) MCQ
28 Q→03True False[1 Marks ]
23 Q→04Fill In The Blanks[1 Marks ]
12 Q→051 Marks Question
27 Q→062 Marks Questions
24 Q→073 Marks Question
13 Q→085 Marks Questions
4 Q→09Case study (4 Marks)
5 Q→Sample Questions
Introduction of Trigonometry questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $\tan\theta = \frac{\text{a}}{\text{b}}$ then $\frac{\cos\theta+\sin\theta}{\cos\theta-\sin\theta}=$
- A$\frac{\text{a}-\text{b}}{\text{a + b}}$
- B$\frac{\text{b}-\text{b}}{\text{b+a}}$
- ✓$\frac{\text{b + a}}{\text{b}-\text{a}}$
- DNone of these
Answer: C.
View full solution →Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as :
Assertion : In a right $\triangle\text{ABC}$, right angled at $B,$ if $ \tan\text{A}=1$, then $ 2\sin\text{A}$. $ \cos\text{A}=1$
Reason : $ \text{cosec}\text { A}$ is the abbreviation used for cosecant of angle $A$.
Assertion : In a right $\triangle\text{ABC}$, right angled at $B,$ if $ \tan\text{A}=1$, then $ 2\sin\text{A}$. $ \cos\text{A}=1$
Reason : $ \text{cosec}\text { A}$ is the abbreviation used for cosecant of angle $A$.
- ABoth assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A).$
- ✓Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A).$
- CAssertion $(A)$ is true but reason $(R)$ is false.
- DAssertion $(A)$ is false but reason $(R)$ is true.
Answer: B.
View full solution →The value of $\frac{\cos^320^\circ-\cos^370^\circ}{\sin^370^\circ-\sin^320^\circ}$ is :
- A$\frac{1}{2}$
- B$\frac{1}{\sqrt{2}}$
- ✓$1$
- D$2$
Answer: C.
View full solution →$\tan10^\circ\tan15^\circ\tan75^\circ\tan80^\circ=?$
- A$\sqrt{3}$
- B$\frac{1}{\sqrt{3}}$
- C$-1$
- ✓$1$
Answer: D.
View full solution →Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R)$. Mark the correct choice as:
Assertion : If $\text{x}\sin^3\theta +\text{y}\cos3\theta = \sin\theta \cos\theta $ and $ \text {x} \sin\theta = \text{y}\cos\theta , $ then $ \text{ x}^2+\text{y}^2=1.$
Reason : For any value of $\theta , \sin^2\theta +\cos^2\theta =1.$
Assertion : If $\text{x}\sin^3\theta +\text{y}\cos3\theta = \sin\theta \cos\theta $ and $ \text {x} \sin\theta = \text{y}\cos\theta , $ then $ \text{ x}^2+\text{y}^2=1.$
Reason : For any value of $\theta , \sin^2\theta +\cos^2\theta =1.$
- ✓Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- BBoth assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- CAssertion $(A)$ is true but reason $(R)$ is false.
- DAssertion $(A)$ is false but reason $(R)$ is true.
Answer: A.
View full solution →Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R)$. Mark the correct choice as:
Assertion : If $\cos\text{A}+\cos^{2}\text{A}=1$ then $\sin^{2}\text{A}+\sin^{4}\text{A}=2.$
Reason : $1-\sin^{2}\text{A}=\cos^{2}\text{A},$ for any value of $A$.
Assertion : If $\cos\text{A}+\cos^{2}\text{A}=1$ then $\sin^{2}\text{A}+\sin^{4}\text{A}=2.$
Reason : $1-\sin^{2}\text{A}=\cos^{2}\text{A},$ for any value of $A$.
- ABoth $A$ and $R$ are true and $R$ is the correct explanation for $A.$
- BBoth $A$ and $R$ are true and $R$ is not the correct explanation for $A.$
- C$A$ is true but $R$ is false.
- ✓$A$ is false but $R$ is true.
Answer: D.
View full solution →Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as :
Assertion : $\frac{(\sin\theta-\cos\theta)(\sin\theta+\cos)}{(\cos\theta-\sin\theta)(\cos\theta+\sin\theta)}=-1.$
Reason : $\sin^{2}\theta+\cos^{2}\theta=-1.$
Assertion : $\frac{(\sin\theta-\cos\theta)(\sin\theta+\cos)}{(\cos\theta-\sin\theta)(\cos\theta+\sin\theta)}=-1.$
Reason : $\sin^{2}\theta+\cos^{2}\theta=-1.$
- A$A$ is true, $R$ is true; $R$ is a correct explanation for $A.$
- B$A$ is true, $R$ is true; $R$ is not a correct explanation for $A.$
- ✓$A$ is true; $R$ is false.
- D$A$ is false; $R$ is true.
Answer: C.
View full solution →Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as :
Assertion : In a right angled triangle, if $\tan\theta=\frac{3}{4}$ then $\sin\theta=\frac{3}{5}.$
Reason : $\sin60^\circ=\frac{1}{2}.$
Assertion : In a right angled triangle, if $\tan\theta=\frac{3}{4}$ then $\sin\theta=\frac{3}{5}.$
Reason : $\sin60^\circ=\frac{1}{2}.$
- ABoth $A$ and $R$ are true and $R$ is the correct explanation for $A.$
- BBoth $A$ and $R$ are true and $R$ is not the correct explanation for $A.$
- ✓$A$ is true but $R$ is false.
- D$A$ is false but $R$ is true.
Answer: C.
View full solution →Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R)$. Mark the correct choice as:
Assertion: In a right angled triangle, if $\tan\theta=\frac{3}{4},$ then greatest side of the triangle is 5 units.
Reason: $(greatest side)^2 = (hypotenuse)^2 = (perpendicular)^2 + (base)^2.$
Assertion: In a right angled triangle, if $\tan\theta=\frac{3}{4},$ then greatest side of the triangle is 5 units.
Reason: $(greatest side)^2 = (hypotenuse)^2 = (perpendicular)^2 + (base)^2.$
- ✓$A$ is true, $R$ is true; $R$ is a correct explanation for $A.$
- B$A$ is true, $R$ is true; $R$ is not a correct explanation for $A.$
- C$A$ is true; $R$ is false.
- D$A$ is false; $R$ is true.
Answer: A.
View full solution →Write ‘True’ or ‘False’ and justify your answer.
$\frac{\tan47^\circ}{\cot43^\circ}=1$
View full solution →$\frac{\tan47^\circ}{\cot43^\circ}=1$
State whether the following are true or false. Justify your answer.$\sin \theta=\frac{4}{3} $ for some angle $\theta.$
View full solution →Write ‘True’ or ‘False’ and justify your answer.
The value of the expression (sin80º - cos80º) is negative.
The value of the expression (sin80º - cos80º) is negative.
Write 'True' or 'False' and justify your answer in the following:
The value of $\sin\theta+\cos\theta$ is always greater than 1.
View full solution →The value of $\sin\theta+\cos\theta$ is always greater than 1.
Write 'True' or 'False' and justify your answer in the following:
The value of the expression $\sin80^\circ-\cos80^\circ$ is negative.
View full solution →The value of the expression $\sin80^\circ-\cos80^\circ$ is negative.
Simplest form of $(1-\cos^2\text{A})(1+\cos^2\text{A})$ is __________.
View full solution →Simplest form of $\frac{1+\tan^2\text{A}}{1+\cot^2\text{A}}$ is _______.
View full solution →If $\tan\text{A}=1,$ then $2\sin\text{A}\cos\text{A}=$ ________.
View full solution →The distance of the point (–3, 4) from Y – axis is _________.
Value of $\frac{2\tan^260^\circ}{1+\tan^230^\circ}$ is __________.
View full solution →Prove the given identity, where the angles involved are acute angles for which the expressions are defined. (cosec A - sin A) (sec A - cos A) = $\frac { 1 } { \tan A + \cot A }$
[Hint: Simplify LHS and RHS separately]
View full solution →[Hint: Simplify LHS and RHS separately]
Prove the given identity, where the angles involved are acute angles for which the expressions are defined. $\frac { \sin \theta - 2 \sin ^ { 3 } \theta } { 2 \cos ^ { 2 } \theta - \cos \theta } = \tan \theta$
View full solution →Prove the given identity, where the angles involved are acute angles for which the expressions are defined. $\sqrt { \frac { 1 + \sin A } { 1 - \sin A } }$ = sec A + tan A
View full solution →Prove the given identity, where the angles involved are acute angles for which the expressions are defined. $\frac { 1 + \sec A } { \sec A } = \frac { \sin ^ { 2 } A } { 1 - \cos A }$
[Hint: Simplify LHS and RHS separately]
View full solution →[Hint: Simplify LHS and RHS separately]
Prove the given identity, where the angles involved are acute angles for which the expressions are defined.
$\left( \frac { 1 + \tan ^ { 2 } A } { 1 + \cot ^ { 2 } A } \right) = \left( \frac { 1 - \tan A } { 1 - \cot A } \right) ^ { 2 }$ $= tan^2 A$
View full solution →$\left( \frac { 1 + \tan ^ { 2 } A } { 1 + \cot ^ { 2 } A } \right) = \left( \frac { 1 - \tan A } { 1 - \cot A } \right) ^ { 2 }$ $= tan^2 A$
Prove the given identity, where the angles involved are acute angles for which the expressions are defined.$\frac{\cos A-\sin A+1}{\cos A+\sin A-1}$ = cosec A + cot A, using the identity $cosec^2 A = 1 + cot^2 A$
View full solution →Prove the given identity, where the angles involved are acute angles for which the expressions are defined. $\frac { \cos A } { 1 + \sin A } + \frac { 1 + \sin A } { \cos A } = 2 \sec A$
View full solution →(1 + tan $\theta$ + sec $\theta$) (1 + cot$\theta$ – cosec$\theta$) =
View full solution →If tan (A + B) = $\sqrt3$ and tan (A - B) = $\frac{1}{\sqrt3}$; 0° < A + B $\leq$ 90°; A > B, then find A and B.
View full solution →Evaluate: $\frac{\sin 30^{\circ}+\tan 45^{\circ}-\ cosec 60^{\circ} }{\sec 30^{\circ}+\cos 60^{\circ}+\cot 45^{\circ}}$
View full solution →Prove the given identities, where the angles involved are acute angles for which the expressions are defined. $(sin A + cosec A)^2 + (cos A + sec A)^2 = 7 + tan^2A + cot^2A$
View full solution →Prove the given identity, where the angles involved are acute angles for which the expressions are defined.$ \frac{{\tan A }}{{1 - \cot A }} + \frac{{\cot A }}{{1 - \tan A }}$ = 1 + sec A cos ecA
[Hint: Write the expression in terms of sin $\theta$ and cos $\theta$]
View full solution →[Hint: Write the expression in terms of sin $\theta$ and cos $\theta$]
Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.
In $\triangle A B C$, right angled at B, if $\tan A = \frac { 1 } { \sqrt { 3 } }$. Find the value of cos A cos C - sin A sin C
View full solution →In $\triangle A B C$, right angled at B, if $\tan A = \frac { 1 } { \sqrt { 3 } }$. Find the value of sin A cos C + cos A sin C.
View full solution →Write all the other trigonometric ratios of $\angle$A in terms of sec A.
View full solution →If 3 cot A = 4, check whether $\frac { 1 - \tan ^ { 2 } A } { 1 + \tan ^ { 2 } A } = \cos ^ { 2 } A - \sin ^ { 2 } A$ or not.
View full solution →Given 15 cot A = 8 find sin A and sec A.
If $ \angle B $ and $\angle Q$ are acute angles such that sin B = sin Q, then prove that $ \angle B = \angle Q$.
View full solution →Ritu's daughter is feeling so hungry and so thought to eat something. She looked into the fridge and found some bread pieces. She decided to make a sandwich. She cut the piece of bread diagonally and found that it forms a right angled triangle, with sides 4cm, $4\sqrt{3}\text{ cm}$ and 8cm.
On the basis of above information, answer the following questions.
- The value of $\angle\text{M}=$
- The value of $\angle\text{K}=$
- Find the value of $\tan\text{M}$.
Or
$\sec^2\text{M}-1=$
Aanya and her father go to meet her friend Juhi for a party. When they reached to Juhi's place, Aanya saw the roof of the house, which is triangular in shape. If she imagined the dimensions of the roof as given in the figure, then answer the following questions.
- If D is the mid point of AC, then BD =
- Measure of $\angle\text{A}=$
- Find the value of $\sin\text{A}+\cos\text{A}$.
Or
Find the value of $\tan^2\text{C}+\tan^2\text{A}$.
Anita, a student of class 10th, has to made a project on 'Introduction to Trigonometry'. She decides to make a bird house which is triangular in shape. She uses cardboard to make the bird house as shown in the figure. Considering the front side of bird house as right angled triangle PQR, right angled at R, answer the following questions.
- If $\angle\text{PQR}=\theta$, then $\cos\theta=$
- The value of $\sec\theta=$
- The value of $\frac{\tan\theta}{1+\tan^2\theta}=$
Or
The value of $\cot^2\theta-\text{cosec}^2\theta=$
Two aeroplanes leave an airport, one after the other. After moving on runway, one flies due North and other flies due South. The speed of two aeroplanes is 400km/ hr and 500km/ hr respectively. Considering PQ as runway and A and B are any two points in the path followed by two planes, then answer the following questions.
- Find $\tan\theta$ if $\angle\text{APQ}=\theta.$
- Find $\cot\text{B}$.
- Find $\tan\text{A}$.
Or
Find $\sec\text{A}$.
Three friends - Anshu, Vijay and Vishal are playing hide and seek in a park. Anshu and Vijay hide in the shrubs and Vishal have to find both of them. If the positions of three friends are at A, B and C respectively as shown in the figure and forms a right angled triangle such that AB = 9 m, BC $=\sqrt{3}\text{ m}$ and $\angle\text{B}=90^\circ$, then answer the following questions.
- The measure of $\angle\text{A}$ is:
- The length of AC is:
- $\cos 2\text{A} =$
Or
$\text{Sin}\Big(\frac{\text{C}}{2}\Big)=$
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