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CBSE - Class 10 Mathematics Introduction to Trigonometry Worksheet

EXERCISE 8.2

Evaluate the following : (v) $\frac{5 \cos^2 60^\circ + 4 \sec^2 30^\circ - \tan^2 45^\circ}{\sin^2 30^\circ + \cos^2 30^\circ}$

State whether the following are true or false. Justify your answer. (iv) $\sin \theta = \cos \theta$ for all values of $\theta$.

Evaluate the following : (iii) $\frac{\cos 45^\circ}{\sec 30^\circ + \text{cosec } 30^\circ}$

Evaluate the following : (iv) $\frac{\sin 30^\circ + \tan 45^\circ – \text{cosec } 60^\circ}{\sec 30^\circ + \cos 60^\circ + \cot 45^\circ}$

State whether the following are true or false. Justify your answer. (i) $\sin (A + B) = \sin A + \sin B$.

Evaluate the following : (ii) $2 \tan^2 45^\circ + \cos^2 30^\circ – \sin^2 60^\circ$

State whether the following are true or false. Justify your answer. (ii) The value of $\sin \theta$ increases as $\theta$ increases.

State whether the following are true or false. Justify your answer. (v) $\cot A$ is not defined for $A = 0^\circ$.

If $\tan (A + B) = \sqrt{3}$ and $\tan (A – B) = \frac{1}{\sqrt{3}}$; $0^\circ < A + B \le 90^\circ$; $A > B$, find $A$ and $B$.

10.

Choose the correct option and justify your choice : (ii) $\frac{1 - \tan^2 45^\circ}{1 + \tan^2 45^\circ} =$

$\tan 90^\circ$

$\sin 45^\circ$

11.

State whether the following are true or false. Justify your answer. (iii) The value of $\cos \theta$ increases as $\theta$ increases.

12.

Choose the correct option and justify your choice : (i) $\frac{2 \tan 30^\circ}{1 + \tan^2 30^\circ} =$

$\sin 60^\circ$

$\cos 60^\circ$

$\tan 60^\circ$

$\sin 30^\circ$

13.

Evaluate the following : (i) $\sin 60^\circ \cos 30^\circ + \sin 30^\circ \cos 60^\circ$

14.

Choose the correct option and justify your choice : (iii) $\sin 2A = 2 \sin A$ is true when $A =$

$0^\circ$

$30^\circ$

$45^\circ$

$60^\circ$

15.

Choose the correct option and justify your choice : (iv) $\frac{2 \tan 30^\circ}{1 - \tan^2 30^\circ} =$

$\cos 60^\circ$

$\sin 60^\circ$

$\tan 60^\circ$

$\sin 30^\circ$

Worksheet Answers

10.

12.

14.

15.

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