Question

Prove the following trigonometric identities.

If cos A + cos² A = 1, prove that sin² A + sin⁴ A = 1

Answer 1

Given : `cos A + cos^2 A = 1`

we have to prove `sin^2 A + sin^4 A = 1`

Now

`cos A + cos^2 A = 1`

`=>cos A = 1 - cos^2 A`

`=> cos A = sin^2 A`

`=> sin^2 A = cos A`

Therefore, we have

`sin^2 A + sin^4 A = cos A + (cos A)^2`

`= cos A + cos^2 A`

= 1

Hence proved.