Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

If cosθ + cos2θ = 1, then

find the value of \(\sqrt {sin^4θ+cos^2θ}\)

Options:

2 cosθ

\(\sqrt {2}\)cosθ

\(\sqrt {2}\)tanθ

\(\frac{\sqrt {2}}{3}\)secθ

Correct Answer:

\(\sqrt {2}\)cosθ

Explanation:

⇒ cosθ = 1- cos2θ = sin2θ

⇒ cosθ = sin2θ and cos2θ = sin4θ

Now,

⇒ \(\sqrt {sin^4θ+cos^2θ}\) = \(\sqrt {cos^2θ+cos^2θ}\) = \(\sqrt {2}\)cosθ