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BITSAT 2011

Exam: BITSAT
Year: 2011
Subject: Mathematics
Chapter: Inverse Trigonometric Functions

BITSAT 2011 · Mathematics · Inverse Trigonometric Functions

The value of ( ( 4 ^ -1 (1)/(3))- ( 2 ^ -1 (1)/(7)) ) is

The value of (\sin

\left(

4 \tan ^{-1}

\frac{1}{3}\right)-\cos \left(

2 \tan ^{-1}

\frac{1}{7}\right)

) is

Options

A $3 / 7$
B $7 / 8$
C $8 / 21$
DNone of these

Correct answer

D. None of these

Step-by-step solution

(\sin \left(

4 \tan ^{-1}

\frac{1}{3}\right)

) (

\begin{aligned} &= 2 \sin \left(2 \tan ^{-1} \frac{1}{3}\right) \cos \left(2 \tan ^{-1} \frac{1}{3}\right)\\ &=2 \sin \left(\tan ^{-1} \frac{3}{4}\right)=\cos \left(\tan ^{-1} \frac{3}{4}\right)=2 \cdot \frac{3}{5} \cdot \frac{4}{5}=\frac{24}{25}\\ \text{ and } \cos \left(2 \tan ^{-1} \frac{1}{7}\right)=\cos \left(\tan ^{-1} \frac{7}{24}\right)=\frac{24}{25} . \end{aligned}

$

) The given expression

=0$

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