Question

If cos A + cos² A = 1, then sin² A + sin⁴ A =

Options

• −1

• 0

• 1

• None of these

Answer 1

Given:

`cos A+cos^2 A=1`

`⇒ 1- cos^2 A= cos A`

So, 

`sin^2 A+sin^4 A` 

`= sin^2 A+sin^2 A sin^2 A` 

`= sin^2  A+(1-cos^2 A)(1-cos^2 A)`

`=sin^2 A+cos A cos A`

`=sin^2 A+cos^2 A`

`=1`