Question

If sin + sin2 + sin3 = 1, then the value of cos6 4cos4 + 8cos2 is x. Find

Answer 1

Step-by-step explanation:

Given If sin x + sin^2 x + sin^3   x = 1, then the value of cos^6 x - 4 cos^4x + 8 cos^2 is x.  

Given sin x + sin^2 x + sin^3 x = 1

So sin x + sin^3 x = 1 – sin^2 x

Sin x(1 + sin^2 x) = cos^2 x

Squaring both sides we get

[sinx (1 + sin^2x)]^2 = (cos^2 x)^2

Sin^2 x (2 – cos^2 x)^2 = cos^4 x

(1 – cos^2 x)(4 – 4cos^2 x + cos^4 x) = cos^4 x

4 – 4 cos^2 x + cos^4 x – cos^2 x(4 – 4 cos^2 x + cos^4 x) = cos^4 x

4 – 4 cos^2 x – 4 cos^2 x + 4 cos^4 x – cos^6 x = 0

4 – 8 cos^2 x + 4 cos^4 x – cos^ 6 x = 0

So cos^6 x – 4 cos^4 x + 8 cos^2 x = 4

Reference link will be

https://brainly.in/question/3046748