If cos x + cos²x = 1, then sin8x + 2 sin6x + sin4x

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If cos x + cos²x = 1, then sin⁸x + 2 sin⁶x + sin⁴x is equal to

1. 0
2. 3
3. 2
4. 1

Correct Option: D

cos x + cos² x = 1
⇒ cos x = 1 – cos² x
= sin² x ....... (i)
∴ sin⁸ x + 2 sin⁶ x + sin⁴ x
= (sin⁴ x + sin² x)²
= ((cos x)² + sin² x)²
= (cos²x + sin² x)²
= 1