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JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

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Application +4 | -1

The value of

\tan \left\{\cos ^{-1} \frac{4}{5}+\tan ^{-1} \frac{2}{5}\right\}

is

\frac{\lambda}{\mu} ;(\lambda, \mu)=1

, then evaluate

\frac{\lambda+19}{\mu}

.

View answer and explanation

Correct option: A

3

Option A (3) is correct because the expression simplifies to

\frac{23}{14}

, so

\lambda = 23

and

\mu = 14

, and

\frac{\lambda+19}{\mu} = 3

.

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\sin \left(\sin ^{-1} \frac{1}{5}+\cos ^{-1} x\right)=1

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2{\tan ^{ - 1}}\left( {\frac{1}{3}} \right) + {\tan ^{ - 1}}\left( {\frac{1}{7}} \right)