Consider and and are respectively minimum and maximum values of and is the point in…

MATHEMATICS · Subjective · CBSE · Mathematics · Inverse Trigonometric Functions · Inverse Trigonometric Functions

Problem

Consider

f(x) = \tan^{-1} \left( \frac{(\sqrt{12} - 2)x^2}{x^4 + 2x^2 + 3} \right)

and

m

and

M

are respectively minimum and maximum values of

f(x)

and

x = a (a > 0)

is the point in the domain of

f(x)

, where

f(x)

attains its maximum value. If

\cos^{-1} x + \cos^{-1} y = 3 \left( \tan^{-1} \left( \tan \frac{7M}{2} \right) + \tan^{-1} \left( m + \tan \frac{3\pi}{8} \right) \right)

, then maximum value of

\frac{3 \sin \theta + 8 \cos \theta}{|x + y|}

is equal to: