Q) If cos A + cos² A = 1, then find the value of sin² A + sin⁴ A.

Ans: cos A + cos² A = 1

cos A = 1 – cos² A

cos A = sin² A…………. (i)

Now, sin² A + sin⁴ A

= (sin² A) + (sin² A) ²

by substituting value from equation (i), we get:

(cos A) + (cos A) ²

= cos A + cos ² A

= 1  (given that cos A + cos² A = 1)

Therefore, the value of sin² A + sin⁴ A = 1.