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 →Question types
Trigonometric Ratios question types
314 questions across 8 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
314
Questions
8
Question groups
5
Question types
01
M.C.Q (1 Marks)
97 Q→02Assertion (A) & Reason (B) MCQ
6 Q→03Fill In The Blanks[1 Marks ]
12 Q→041 Marks Question
27 Q→052 Marks Questions
79 Q→063 Marks Question
71 Q→075 Marks Questions
19 Q→08Case study (4 Marks)
3 Q→Sample Questions
Trigonometric Ratios questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
$\tan5^\circ\times\tan30^\circ\times4\tan85^\circ$ is equal to:
- ✓$\frac{4}{\sqrt{3}}$
- B$4\sqrt{3}$
- C$1$
- D$4$
Answer: A.
View full solution →The value of $\tan1^\circ\tan2^\circ\tan3^\circ.....\tan89^\circ$ is:
- ✓1
- B-1
- C0
- DNone of these
Answer: A.
View full solution →If $\text{x}\tan45^\circ\cos60^\circ=\sin60^\circ\cot60^\circ,$ then x is equal to:
- ✓$1$
- B$\sqrt{3}$
- C$\frac{1}{2}$
- D$\frac{1}{\sqrt{2}}$
Answer: A.
View full solution →$\frac{2\tan30^\circ}{1-\tan^230^\circ}$ is equal to:
- A$\cos60^\circ$
- B$\sin60^\circ$
- ✓$\tan60^\circ$
- D$\sin30^\circ$
Answer: C.
View full solution →Statement-1 (A): For $0 \leq \theta < 90^{\circ}, \sec x+\cos x \geq 2$.
Statement-2 (R): For any $x > 0, x+\frac{1}{x} \geq 2$.
Statement-2 (R): For any $x > 0, x+\frac{1}{x} \geq 2$.
- ✓Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is True, Statement-2 is False.
- DStatement-1 is False, Statement-2 is True.
Answer: A.
View full solution →Statement-1 (A): For any acute angle $\theta$, the value of $\sin \theta$ cannot be greater than 1.
Statement-2 (R): Hypotenuse is the longest side in any right angled triangle.
Statement-2 (R): Hypotenuse is the longest side in any right angled triangle.
- ✓Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is True, Statement-2 is False.
- DStatement-1 is False, Statement-2 is True.
Answer: A.
View full solution →Statement-1 (A): In Fig.9.16, the trigonometric ratios of angle $\theta$ depend only on the value of $\theta$ and are independent of the position of the point $P$ on the terminal side $A Y$ of angle $\theta$.
Statement-2 (R) : In a right triangle $A B C$ right angled at $B$, if $\angle B A C=\theta$, then $\sin \theta=\frac{B C}{A C} < 1$ and $\cos \theta=\frac{A B}{A C} < 1$ because the hypotenuse $A C_{\text {is }}$ the longest side.
Statement-2 (R) : In a right triangle $A B C$ right angled at $B$, if $\angle B A C=\theta$, then $\sin \theta=\frac{B C}{A C} < 1$ and $\cos \theta=\frac{A B}{A C} < 1$ because the hypotenuse $A C_{\text {is }}$ the longest side.
- AStatement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- ✓Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is True, Statement-2 is False.
- DStatement-1 is False, Statement-2 is True.
Answer: B.
View full solution →Statement-1 (A): For $0<\theta \leq 90^{\circ}, \sin \theta+\operatorname{cosec} \theta \geq 2$.
Statement-2 (R): $\quad x+\frac{1}{x} \geq 2$ for all $x>0$.
Statement-2 (R): $\quad x+\frac{1}{x} \geq 2$ for all $x>0$.
- ✓Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is true, Statement- 2 is false.
- DStatement-1 is false, Statement-2 is true.
Answer: A.
View full solution →Statement-1 (A): For any acute angle $\theta\left(0 \leq \theta<90^{\circ}\right), \sec \theta \geq 1$
Statement-2 (R): For any acute angle $\theta\left(0<\theta \leq 90^{\circ}\right), \operatorname{cosec} \theta \geq 1$
Statement-2 (R): For any acute angle $\theta\left(0<\theta \leq 90^{\circ}\right), \operatorname{cosec} \theta \geq 1$
- AStatement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- ✓Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is true, Statement- 2 is false.
- DStatement-1 is false, Statement-2 is true.
Answer: B.
View full solution →If $\triangle ABC$ is an isosceles right triangle right angled at $B$, then $\frac{\tan A+\cot C}{\cot A+\cot C}$ ____________ .
View full solution →If $\sin (A+B)=\cos (A-B)=\frac{\sqrt{3}}{2}$, then $\cot 2 A$ = ____________ .
View full solution →If $\sin \theta+\cos \theta=1$ and $0^{\circ} \leq \theta \leq 90^{\circ}$, then the possible values of $\theta$ are ____________ .
View full solution →If $\tan \theta+\cot \theta=2$ and, $0^{\circ}<\theta<90^{\circ}$ then $\tan ^{10} \theta+\cot ^{10} \theta$ is equal to ____________ .
View full solution →The value of $\cos 1^{\circ} \cos 2^{\circ} \cos 3^{\circ} \ldots \cos 120^{\circ}$ is ____________ .
View full solution →What is the maximum value of $\frac{1}{\sec\theta}?$
View full solution →Write the maximum and minimum values of $\sin\theta.$
View full solution →In Fig. 9.45, $P S=3 cm, Q S=4 cm, \angle P R Q=\theta, \angle P S Q=90^{\circ}, P Q \perp R Q$ and $R Q=9 cm$. Evaluate $\tan \theta$.
View full solution →If $x \sin 60^{\circ}+\cos 30^{\circ}-\tan 45^{\circ}=\frac{\sqrt{3}}{2}$, find the value of $x$.
View full solution →If $\tan A=\sqrt{3}$, then find the value of $\cos ^2 A-\sin ^2 A$.
View full solution →Evaluate the following:
$\frac{\sec70^\circ}{\text{cosec }20^\circ}+\frac{\sin59^\circ}{\cos31^\circ}$
View full solution →$\frac{\sec70^\circ}{\text{cosec }20^\circ}+\frac{\sin59^\circ}{\cos31^\circ}$
Express the following in terms of trigonometric ratios of angles lying between 0° and 45°.$\cos78^\circ+\sec78^\circ$
View full solution →Evaluate the following:
$\text{cosec 31}^\circ-\sec59^\circ$
View full solution →$\text{cosec 31}^\circ-\sec59^\circ$
Find the value of x in the following:
$\cos2\text{x}=\cos60^\circ\cos30^\circ+\sin60^\circ\sin30%\circ$
View full solution →$\cos2\text{x}=\cos60^\circ\cos30^\circ+\sin60^\circ\sin30%\circ$
Evaluate:
$=\frac{\sin50^\circ}{\cos40^\circ}+\frac{\text{cosec }40^\circ}{\sec50^\circ}-4 \cos50^\circ\ \text{cosec }40^\circ$
View full solution →$=\frac{\sin50^\circ}{\cos40^\circ}+\frac{\text{cosec }40^\circ}{\sec50^\circ}-4 \cos50^\circ\ \text{cosec }40^\circ$
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
$\tan\theta=11$
View full solution →$\tan\theta=11$
If $\sec\text{A}=\frac{17}{8},$ verify that $\frac{3-4\sin^2\text{A}}{4\cos^2\text{A}-3}=\frac{3-\tan^2\text{A}}{1-3\tan^2\text{A}}.$
View full solution →Evaluate the following:
$\frac{\tan45^\circ}{\text{cosec}30^\circ}+\frac{\sec60^\circ}{\cot45^\circ}-\frac{5\sin90^\circ}{2\cos0^\circ}$
View full solution →$\frac{\tan45^\circ}{\text{cosec}30^\circ}+\frac{\sec60^\circ}{\cot45^\circ}-\frac{5\sin90^\circ}{2\cos0^\circ}$
If A = 30° and B = 60°, verify that.
$\sin(\text{A}+\text{B})=\sin\text{A}\cos\text{B}+\cos\text{A}\sin\text{B}$
View full solution →$\sin(\text{A}+\text{B})=\sin\text{A}\cos\text{B}+\cos\text{A}\sin\text{B}$
If $\tan\theta=\frac{20}{21},$ show that $\frac{1-\sin\theta+\cos\theta}{1+\sin\theta+\cos\theta}=\frac{3}{7}.$
View full solution →If $\sec\theta=\frac{5}{4},$ find the value of $\frac{\sin\theta-2\cos\theta}{\tan\theta-\cot\theta}.$
View full solution →In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
$\sec\theta=\frac{13}{5}$
View full solution →$\sec\theta=\frac{13}{5}$
If $3\cot\theta=2,$ find the value of $\frac{4\sin\theta-3\cos\theta}{2\sin\theta+6\cos\theta}.$
View full solution →In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
$\cot\theta=\frac{12}{5}$
View full solution →$\cot\theta=\frac{12}{5}$
If $\cos\theta=\frac{3}{5},$ find the value of $\frac{\sin\theta-\frac{1}{\tan\theta}}{2\tan\theta}.$
View full solution →Kite festival is celebrated in many countries at different times of the year. In India, every year 14 th January is celebrated as International Kite Day. On this day many people visit India and participate in the festival by flying various kinds of kites. The picture given below, shows kites flying together.
In Fig. the angles of elevation of two kites (Points A and B) from the hands of a man (Point C) are found to be $30^{\circ}$ and $60^{\circ}$ respectively. Taking $A D=50 m$ and $B E=60 m$, find
(i) the lengths of strings used (take them straight) for kites $A$ and $B$ as shown in the figure.
(ii) the distance ' $d$ ' between these two kites.
View full solution →In Fig. the angles of elevation of two kites (Points A and B) from the hands of a man (Point C) are found to be $30^{\circ}$ and $60^{\circ}$ respectively. Taking $A D=50 m$ and $B E=60 m$, find
(i) the lengths of strings used (take them straight) for kites $A$ and $B$ as shown in the figure.
(ii) the distance ' $d$ ' between these two kites.
A trolley carries passengers from the ground level located at point $\Lambda$ to up to the top of mountain chateau located at $P$ as shown in Fig. The point $A$ is at a distance of 2000 m from point $C$ at the base of mountain. Here $\alpha=30^{\circ}, \beta=60^{\circ}$.
(i) Assuming the cable is held tight what will be the length of cable?
(a) 2000 m $\qquad$ (b) $2000 \sqrt{3} m$ $\qquad$ (c) $4000 \sqrt{3} m$ $\qquad$ (d) $\frac{4000}{\sqrt{3}} m$
(ii) What will be height of the mountain?
(a) 1000 m $\qquad$ (b) $\frac{2000}{\sqrt{3}} m$ $\qquad$ (c) 2000 m $\qquad$ (d) $2000 \sqrt{3} m$
(iii) What will be the slant height of the mountain?
(a) 4000 m $\qquad$ (b) $\frac{4000}{3} m$ $\qquad$ (c) $4000 \sqrt{3} m$ $\qquad$ (d) $\frac{4000}{\sqrt{3}} m$
(iv) What will be the length of $B C$ ?
(a) 1000 m $\qquad$ (b) $\frac{2000}{3} m$ $\qquad$ (c) $1000 \sqrt{3} m$ $\qquad$ (d) $\frac{1000}{\sqrt{3}} m$
View full solution →(i) Assuming the cable is held tight what will be the length of cable?
(a) 2000 m $\qquad$ (b) $2000 \sqrt{3} m$ $\qquad$ (c) $4000 \sqrt{3} m$ $\qquad$ (d) $\frac{4000}{\sqrt{3}} m$
(ii) What will be height of the mountain?
(a) 1000 m $\qquad$ (b) $\frac{2000}{\sqrt{3}} m$ $\qquad$ (c) 2000 m $\qquad$ (d) $2000 \sqrt{3} m$
(iii) What will be the slant height of the mountain?
(a) 4000 m $\qquad$ (b) $\frac{4000}{3} m$ $\qquad$ (c) $4000 \sqrt{3} m$ $\qquad$ (d) $\frac{4000}{\sqrt{3}} m$
(iv) What will be the length of $B C$ ?
(a) 1000 m $\qquad$ (b) $\frac{2000}{3} m$ $\qquad$ (c) $1000 \sqrt{3} m$ $\qquad$ (d) $\frac{1000}{\sqrt{3}} m$
In structural design a structure is composed of triangles that are interconnecting. A truss is one of the major types of engineering structures and is especially used in the design of bridges and buildings. Trusses are designed to support loads, such as the weight of people. A truss is exclusively made of long, straight members connected by joints at the end of each member.
This is a single repeating triangle in a truss system.
(i) In above triangle, what is the length of $A C$ ?
(a) 5 ft $\qquad$ (b) 6 ft $\qquad$ (c) 8 ft $\qquad$ (d) $\frac{8}{\sqrt{3}} ft$
(ii) What is the length of $B C$ ?
(a) $\frac{4}{\sqrt{3}} ft$ $\qquad$ (b) $4 \sqrt{3} ft$ $\qquad$ (c) 8 ft $\qquad$ (d) $8 \sqrt{3} ft$
(iii) If $\sin \Lambda=\sin C$, what will be the length of $B C$ ?
(a) 2 fl $\qquad$ (b) 4 ff $\qquad$ (c) 8 ft $\qquad$ (d) $4 \sqrt{2} ft$
(iv) Which of the following relation will be Irue in the triangle?
(a) $\sin \left(\frac{A+C}{2}\right)=\cos \left(\frac{B}{2}\right)$
(b) $\sin \left(\frac{A+B}{2}\right)=\sin \left(\frac{C}{2}\right)$
(c) $\cos \left(\frac{A+B}{2}\right)=\cos \left(\frac{C}{2}\right)$
(d) $\cos \left(\frac{A-B}{2}\right)=\cos \left(\frac{C}{2}\right)$
View full solution → This is a single repeating triangle in a truss system.
(i) In above triangle, what is the length of $A C$ ?
(a) 5 ft $\qquad$ (b) 6 ft $\qquad$ (c) 8 ft $\qquad$ (d) $\frac{8}{\sqrt{3}} ft$
(ii) What is the length of $B C$ ?
(a) $\frac{4}{\sqrt{3}} ft$ $\qquad$ (b) $4 \sqrt{3} ft$ $\qquad$ (c) 8 ft $\qquad$ (d) $8 \sqrt{3} ft$
(iii) If $\sin \Lambda=\sin C$, what will be the length of $B C$ ?
(a) 2 fl $\qquad$ (b) 4 ff $\qquad$ (c) 8 ft $\qquad$ (d) $4 \sqrt{2} ft$
(iv) Which of the following relation will be Irue in the triangle?
(a) $\sin \left(\frac{A+C}{2}\right)=\cos \left(\frac{B}{2}\right)$
(b) $\sin \left(\frac{A+B}{2}\right)=\sin \left(\frac{C}{2}\right)$
(c) $\cos \left(\frac{A+B}{2}\right)=\cos \left(\frac{C}{2}\right)$
(d) $\cos \left(\frac{A-B}{2}\right)=\cos \left(\frac{C}{2}\right)$
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