QJEEM08Mab542: JEE Main 2008 Mathematics - Class 12 JEEM08Mab542 Solution

Question

Verified Solution • 2025–26 Session moderate

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}}

Step-by-Step Verified Solution