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Free CBSE - Class 10 Mathematics - Introduction to Trigonometry worksheets

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1.

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

1.

$\sin 60^\circ$

2.

$\cos 60^\circ$

3.

$\tan 60^\circ$

4.

$\sin 30^\circ$

2.

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

1.

$0^\circ$

2.

$30^\circ$

3.

$45^\circ$

4.

$60^\circ$

3.

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

1.

$\cos 60^\circ$

2.

$\sin 60^\circ$

3.

$\tan 60^\circ$

4.

$\sin 30^\circ$

4.
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 $B$.
5.
State whether the following are true or false. Justify your answer. (i) $\sin (A + B) = \sin A + \sin B$.
6.
State whether the following are true or false. Justify your answer. (ii) The value of $\sin \theta$ increases as $\theta$ increases.
7.
State whether the following are true or false. Justify your answer. (iii) The value of $\cos \theta$ increases as $\theta$ increases.
8.
State whether the following are true or false. Justify your answer. (iv) $\sin \theta = \cos \theta$ for all values of $\theta$.
9.
State whether the following are true or false. Justify your answer. (v) $\cot A$ is not defined for $A = 0^\circ$.
10.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (x) $(\frac{1 + \tan^2 A}{1 + \cot^2 A}) = (\frac{1 - \tan A}{1 - \cot A})^2 = \tan^2 A$
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