The value of [cot( ec^ - 15 3 + ^ - 12 3 )] is :

Question

The value of $$cot\left( {\cos e{c^{ - 1}}{5 \over 3} + {{\tan }^{ - 1}}{2 \over 3}} \right)$$ is :

Accepted Answer

Given,

$$Cot\left( {so{{\sec }^{ - 1}}{5 \over 3} + {{\tan }^{ - 1}}{2 \over 3}} \right)$$

$$ = \cot \left( {{{\tan }^{ - 1}}{3 \over 4} + {{\tan }^{ - 1}}{2 \over 3}} \right)$$

$$ = cot\left( {{{\tan }^{ - 1}}{{{3 \over 4} + {2 \over 3}} \over {1 - {3 \over 4} - {2 \over 3}}}} \right)$$

$$ = \cot \left( {{{\tan }^{ - 1}}\left( {{{17} \over 6}} \right)} \right)$$

$$ = \cot \left( {{{\cot }^{ - 1}}{6 \over {17}}} \right)$$

$$ = {6 \over {17}}$$

Solutions · 1