# Trigonometry Problems set1

In this page trigonometry problems set1 we are going to see practice questions in this topic .Here we you can find solution with detailed explanation.

## Identities of Trigonometry

Let us see trigonometric-identities

1. sin² θ  + cos² θ = 1
2. sin² θ  = 1 - cos² θ
3. cos² θ = 1 - sin² θ
4. Sec² θ - tan² θ = 1
5. Sec² θ  = 1 +  tan² θ
6. tan² θ  =  Sec² θ - 1
7. Cosec² θ - cot² θ = 1
8. Cosec² θ = 1 + cot² θ
9. cot² θ =  Cosec² θ - 1

These identities are applied in both ways ,left to right or right to left.So we have to memories all the identities.

Question 1

Prove that (1 - cos² θ) Cosec² θ = 1

Solution:

L.H.S

= (1 - cos² θ) Cosec² θ

 We can write sin² θ instead of (1-cos² θ)

= (sin² θ) Cosec² θ

 trigonometry problems set1 We can write 1/sin² θ instead of cosec² θ

=  (sin² θ) 1/sin² θ

=  sin² θ/sin² θ

= 1

R.H.S

Question 2

Prove that (1 + cot² θ) sin² θ = 1

Solution:

L.H.S

= (1 + cot² θ) sin² θ

 From this identity we come to know 1+cot²θ=Cosec²θ

= Cosec² θ x sin² θ

= (1/sin² θ) (sin² θ)

=  sin² θ/sin² θ

= 1

R.H.S

Question 3

Prove that (sec² θ -1) cot² θ = 1

Solution:

L.H.S

= (sec² θ -1) cot² θ

 From this identity we come to know sec²θ -1 =tan²θ

=  tan²θ x cot² θ

 We can write 1/tan² θ instead of cot² θ

=  tan² θ (1/tan² θ)

=  tan² θ/tan² θ

= 1

R.H.S

Question 4

Prove that (1 - cos θ)(1 + cos θ)(1 + cot² θ) = 1

Solution:

L.H.S

= (1 - cos θ) (1 + cos θ) (1 + cot² θ)

From this we can write (1-cos²θ) instead of (1 - cos θ) (1 + cos θ)

=  (1 - cos²θ) x (1 + cot² θ)

 From this identity we come to know 1+cot²θ=cosec²θ

=  sin² θ (cosec² θ)

=  sin² θ(1/sin² θ)

= (sin² θ/sin² θ)

= 1

R.H.S

Question 5

Prove that Sec θ √(1 - sin ²θ) = 1

Solution:

L.H.S

= Sec θ √(1 - sin ²θ)

 We can write cos² θ instead of (1-sin² θ)

=  sec θ √cos ² θ

=  sec θ cos θ

 We can write 1/cosθ instead of sec θ

=  (1/cos θ) cos θ

= (cos θ/cos θ)

= 1

R.H.S

Trigonometry Problems set1 to Set2