If ${\tan ^{ - 1}}a + {\tan ^{ - 1}}b = {\sin ^{ - 1}}1 - {\tan ^{ - 1}}c$, then

JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

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Application +4 | -1

{\tan ^{ - 1}}a + {\tan ^{ - 1}}b = {\sin ^{ - 1}}1 - {\tan ^{ - 1}}c

, then

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Correct option: C

\frac{1}{a} + \frac{1}{b} + \frac{1}{c} - \frac{1}{{abc}} = 0

Option C (

\frac{1}{a} + \frac{1}{b} + \frac{1}{c} - \frac{1}{{abc}} = 0

) is correct because it is the result of simplifying the given equation using the tangent addition formula and the fact that

{\sin ^{ - 1}}1 = \frac{\pi}{2}

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