Question

solve .

full solution required.

Answer 1

Given : sinx + sin^2x = 1.

⇒ sinx = 1 - sin^2x

⇒ sinx = cos^2x    ----- (1)

Now,

Given : cos^12x + 3cos^10x + 3cos^8x + cos^6x - 1.

⇒ (cos^4x)^3 + 3(cos^4x)^2(cos^2x) + 3(cos^4x)(cos^2x)^2 + (cos^2x)^3 - 1

∴ We know that a^3 + 3a^2b + 3ab^2 + b^3 = (a + b)^3

⇒ (cos^4x + cos^2x)^3

⇒ ((cos^2x)^2 + cos^2x)^3

⇒ (sin^2x + cos^2x)^3  {From (1)}

⇒ 1.

Therefore, the answer is 1.  ------ Option (2).

Hope it helps!