# Trigonometry Problems set2

In this page trigonometry problems set2 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 6

Prove that cosec θ √(1 - cos²θ) = 1

Solution:

L.H.S

= cosec θ √(1 - cos²θ)

 We can write sin ² θ instead of 1 - cos²θ.

=  cosec θ √sin ² θ

We can take one sin θ from the radical sign.

=  cosec θ sin θ

we can write 1/sin θ instead of cosec θ.

=  (1/sin θ) sin θ

= (sin θ/sin θ)

= 1

R.H.S

Question 7

Prove that (1 - cos²θ) sec²θ = tan²θ

Solution:

L.H.S

= (1 - cos²θ) sec²θ

 We can write sin ² θ instead of 1 - cos²θ.

=  sin²θ sec²θ

 trigonometry problems set2 we can write 1/cos ²θ instead of sec² θ.

=  sin²θ (1/cos²θ)

=  (sin²θ /cos²θ)

= tan²θ

R.H.S

Question 8

Prove that (sec²θ-1) (cosec²θ-1) = 1

Solution:

L.H.S

= (sec²θ-1) (cosec²θ-1)

 we can write tan²θ instead of (sec² θ - 1). we can write cot²θ instead of (cosec² θ - 1).

= (tan²θ) (cot²θ)

 we can write 1/tan²θ instead of cot² θ.

= (tan²θ) (1/tan²θ)

= (tan²θ/tan²θ)

= 1

R.H.S

Question 9

Prove that secθ (1 - sinθ) (secθ + tan θ) = 1

Solution:

L.H.S

= sec θ (1 - sin θ) (secθ + tan θ)

 We can write 1/cos θ instead of sec θ

= (1/cos θ) (1 - sin θ) (secθ + tan θ)

 We can write sin θ/cos θ instead of tan θ

= (1/cos θ) (1 - sin θ) [(1/cos θ) + (sin θ/cosθ)]

Now we are going to take L.C.M

= (1/cos θ) (1 - sin θ) [(1 + sin θ)/cosθ]

= (1 - sin θ)/cos θ  [(1 + sin θ)/cosθ]

 From this identity we can write 1 - sin²θ instead of (1 + sinθ) (1 - sinθ)

= (1 - sin²θ)/cos² θ

 We can write cos² θ  instead of 1 - sin² θ

= (cos² θ )/cos² θ

= 1

R.H.S

Trigonometry Problems Set2 to Trigonometry