SSC CGL Model Paper 1

© examsiri.com

Question : 66 of 100

Marks: +1, -0

If

\sinθ + \sin^2 θ + \sin^3 θ = 1.

Find

\cos^6θ-4 \cos^4θ+8 \cos^2 θ = ?

0
2
4
6

Solution:

\Sinθ + \Sin^2 θ + \Sin^3 θ = 1

⇒

\Sinθ + \Sin^3 θ = 1- \Sin^2 θ

⇒

\Sinθ[1 + \Sin^2θ] = \Cos^2θ

⇒

\Sinθ[2 - \cos^2θ] = \cos^2θ

On squaring both sides

\Sin^2θ[2 - \cos^2θ] ^2= \cos^4θ

⇒

(1 -\cos^2θ)[4 + \cos^4 θ-4 \cos^2 θ]

= \cos^4θ

⇒

4 + \cos^4 θ -4 \cos^2θ -4\cos^2θ

-\cos^6 θ +4 \cos^4 θ = \cos^4 θ

⇒

\cos^6 θ -4 \cos^4θ + 8\cos^2θ = 4

© examsiri.com

Go to Question:

Prev Question

Next Question