Question

................solve this .............................................​

Answer 1

Answer:

B) 1

Step-by-step explanation:

Given :

If sin x + sin² x = 1 then,

Value of cos⁸ x + 2cos⁶ x + cos⁴ x is .

Solution :

_

We know that,

sin² x + cos² x = 1

⇒ 1 - sin² x = cos² x,

(a + b)² = a² + 2ab + b²

__

sin x + sin² x = 1

⇒ sin x =1 - sin² x

⇒ sin x = cos² x ..(i)

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cos⁸ x + 2cos⁶ x + cos⁴

⇒ (cos⁴ x)² + 2(cos⁴ x)(cos² x) + (cos² x)²

⇒ (cos⁴ x + cos² x)²

⇒ ( (cos² x)² + (cos² x) )

⇒ (sin² x + sin x)²       (from (i) )

⇒ (1)² = 1                      (given)