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Free CBSE - Class 10 Mathematics Introduction to Trigonometry EXERCISE 8.3 worksheets

Sample Worksheets

Here is a Sample Worksheet for you to Practice. Download this worksheet to see the answers.

1.
Express the trigonometric ratios $\sin A$, $\sec A$ and $\tan A$ in terms of $\cot A$.
2.
Write all the other trigonometric ratios of $\angle A$ in terms of $\sec A$.
3.

Choose the correct option. Justify your choice. (i) $9 \sec^2 A – 9 \tan^2 A =$

1.

1

2.

9

3.

8

4.

0

4.

Choose the correct option. Justify your choice. (ii) $(1 + \tan \theta + \sec \theta) (1 + \cot \theta – \text{cosec } \theta) =$

1.

0

2.

1

3.

2

4.

–1

5.

Choose the correct option. Justify your choice. (iii) $(\sec A + \tan A) (1 – \sin A) =$

1.

$\sec A$

2.

$\sin A$

3.

$\text{cosec } A$

4.

$\cos A$

6.

Choose the correct option. Justify your choice. (iv) $\frac{1 + \tan^2 A}{1 + \cot^2 A} =$

1.

$\sec^2 A$

2.

–1

3.

$\cot^2 A$

4.

$\tan^2 A$

7.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (i) $(\text{cosec } \theta – \cot \theta)^2 = \frac{1 - \cos \theta}{1 + \cos \theta}$
8.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (ii) $\frac{\cos A}{1 + \sin A} + \frac{1 + \sin A}{\cos A} = 2 \sec A$
9.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (iii) $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \sec \theta \text{cosec } \theta$
[Hint : Write the expression in terms of $\sin \theta$ and $\cos \theta$]
10.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined. (iv) $\frac{1 + \sec A}{\sec A} = \frac{\sin^2 A}{1 – \cos A}$
[Hint : Simplify LHS and RHS separately]
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