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