JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

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Application +4 | -1

\cos ^{-1} \frac{p}{a}+\cos ^{-1} \frac{q}{b}=\alpha

and

\frac{\mathrm{p}^2}{\mathrm{a}^2}-\frac{2 \mathrm{pq}}{\mathrm{ab}} \cos \alpha+\frac{\mathrm{q}^2}{\mathrm{~b}^2}=\mathrm{f}(\alpha)

, then number of integers in the range of

f(\alpha)

View answer and explanation

Correct option: A

Option A (1) is correct because by simplifying the integral using trigonometric substitutions, we find that A = 1/2 and B = 1/2, so A+B = 1.

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x

{x^2} + {y^2} + {z^2} = {r^2},

{\tan ^{ - 1}}\left( {\frac{{xy}}{{zr}}} \right) + {\tan ^{ - 1}}\left( {\frac{{yz}}{{xr}}} \right) + {\tan ^{ - 1}}\left( {\frac{{xz}}{{yr}}} \right)\;

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