If cos θ + cos^2 θ = 1 then the value of sin^2 θ + sin^4 θ is (A) -1 (B) 1

Question

If \(\cos \theta + \cos^2 \theta = 1\) then the value of \(\sin^2\theta + \sin^4\theta \) is

(A) -1

(B) 1

(C) 0

(D) 2

Answer 1

Correct option is : (B) 1

Given,

\(\cos \theta+\cos ^2 \theta =1 \)

\(\cos \theta =1-\cos ^2 \theta \)

\(\cos \theta =\sin ^2 \theta \quad [\because \sin^2 \theta + \cos^2\theta=1]\)

\(\therefore \sin^2\theta=\cos \theta\)

Now,

\( \sin ^2 \theta+\sin ^4 \theta \)

\(= \cos \theta+\left(\sin ^2 \theta\right)^2 \)

\(= \cos \theta+\cos ^2 \theta \)

= 1

Answer 2

Correct option is : (B) 1