If the functions and are defined from to such that and

MATHEMATICS · Single correct · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

If the functions

f(x)

and

g(x)

are defined from

\mathbb{R}

to

\mathbb{R}

such that

f(x)=\cos^2x+\cos^2\left(x+\frac{2\pi}{3}\right)+\cos^2\left(x-\frac{2\pi}{3}\right)+\cos^2\frac{5\pi}{4}

and

g(2)=-1

, then the value of

\cot^{-1}(g(f(1)))+\cos^{-1}(g(f(2)))

is equal to (a)

\frac{3\pi}{4}

(b)

\frac{5\pi}{4}

(c)

\frac{3\pi}{2}

(d)

\frac{7\pi}{4}

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