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BITSAT 2023Paper 1

Exam: BITSAT
Year: 2023
Paper: Paper 1
Subject: Mathematics
Chapter: Inverse Trigonometric Functions

BITSAT 2023 · Paper 1 · Mathematics · Inverse Trigonometric Functions

^ -1 ((1)/(4))+ ^ -1 ((2)/(9))is equal to

\tan ^{-1} \left(\frac{1}{4}\right)+\tan ^{-1} \left(\frac{2}{9}\right)is equal to

Options

A $\frac{1}{2} \cos ^{-1} \left(\frac{3}{5}\right)$
B $\frac{1}{2} \sin ^{-1} \left(\frac{3}{5}\right)$
C $\frac{1}{2} \tan ^{-1} \left(\frac{3}{5}\right)$
D $\tan ^{-1} \left(\frac{1}{2}\right)$

Correct answer

D. $\tan ^{-1} \left(\frac{1}{2}\right)$

Step-by-step solution

\tan ^{-1}\left(\frac{1}{4}\right)+\tan ^{-1}

\left(\frac{2}{9}\right)=\tan ^{-1}\left\{\frac{\frac{1}{4}+\frac{2}{9}}{1-\frac{1}{4} \times \frac{2}{9}}\right\}

<br />

=\tan ^{-1} \left\ {\frac{9+8}{36-2}\right\}

=\tan ^{-1} \left(\frac{1}{2}\right)

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