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BITSAT 2012

Exam: BITSAT
Year: 2012
Subject: Mathematics
Chapter: Inverse Trigonometric Functions

BITSAT 2012 · Mathematics · Inverse Trigonometric Functions

If k ≤ ^ -1 x+ ^ -1 x+ ^ -1 x ≤ K, then -

If

k \leq \sin ^{-1} x+\cos ^{-1} x+\tan ^{-1} x \leq K,

then

-

Options

A $\mathrm{k}=0, \mathrm{ K}=\pi$
B $\mathrm{k}=0, \mathrm{ K}=\pi / 2$
C $\mathrm{k}=\pi / 2, \mathrm{ K}=\pi$
DNone of these

Correct answer

D. None of these

Step-by-step solution

\sin ^{-1} x+\cos ^{-1} x+\tan ^{-1} x=\frac{\pi}{2}+\tan ^{-1} x

Since domain of the function

\mathrm{x} \in[-1,1]\therefore-\frac{\pi}{4} \leq \tan ^{-1} x \leq \frac{\pi}{4}

Hence,

\mathrm{k}=\frac{\pi}{4}

and

\mathrm{K}=\frac{3 \pi}{4}

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