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Range of Trigonometric Expressions

tan -12+tan -...

Question

${tan}^{- 1} 2 + {tan}^{- 1} 3 = c o s e c^{- 1} x$ , then x is equal to -

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\sqrt{2}

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\sqrt{2}

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none of these

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Solution

The correct option is D none of these
Given, ${tan}^{- 1} 2 + {tan}^{- 1} 3 = c o s e c^{- 1} x$
$\Rightarrow π + {tan}^{- 1} (- 1) = c o s e c^{- 1} x$
$\Rightarrow π - \frac{π}{4} = c o s e c^{- 1} x \Rightarrow \frac{3 π}{4} = c o s e c^{- 1} x$
$\Rightarrow$ no solution. ${- \frac{π}{2} \leq c o s e c^{- 1} x \leq \frac{π}{2}}$

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