Question

If cos A + cos² A = 1 then (sin² A + sin⁴ A) = ?

(a) 1/2

(b) 2

(c) 1

(d) 4

Answer 1

Correct answer = (c) 1

cos² A + A = 1

⇒ cos A = sin² A ......(i)

squaring both sides of (i), we get:

cos² A = sin⁴ A......(ii)

Adding (i) and (ii), we get:

sin² A + sin⁴ A = cos A + cos² A

⇒ sin² A + sin⁴ A = 1   [∵ cos A + cos² A = 1]