Question

If sin²x + sinx = 1, then cos¹²x + 3cos¹⁰ x + 3cos⁸x + cos⁶x – 1 is equal to 

(A) 1 

(B) 0 

(C) –1 

(D) none of these 

Answer 1

Correct option (B) 0

Explanation:

sin²x + sin x = 1 ⇒ sin x = cos² x cos¹² x + 3 cos¹⁰ x + 3 cos⁸ x + cos⁶ x – 1 = (sin⁶ x) + 3 sin⁵ x + 3 sin⁴ x + (sin³ x) – 1 

= (sin² x)³ + 3(sin² x)² sin x + 3sin² x sin² x + (sin x)³ – 1 = (sin² x + sin x)³ – 1 = 1 – 1 = 0