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Question: \(\cot ^ { - 1 } 3 + \operatorname { cosec } ^ { - 1 } \sqrt { 5 }\)=...

cot⁡−13+cosec⁡−15\cot ^ { - 1 } 3 + \operatorname { cosec } ^ { - 1 } \sqrt { 5 }=

A

π3\frac { \pi } { 3 }

B

π4\frac { \pi } { 4 }

C

π6\frac { \pi } { 6 }

D

π2\frac { \pi } { 2 }

Answer

π4\frac { \pi } { 4 }

Explanation

Solution

cot⁡−13+cosec⁡−15=cot⁡−13+cot⁡−12\cot ^ { - 1 } 3 + \operatorname { cosec } ^ { - 1 } \sqrt { 5 } = \cot ^ { - 1 } 3 + \cot ^ { - 1 } 2

=cot⁡−1(3×2−13+2)=cot⁡−1(1)=π4= \cot ^ { - 1 } \left( \frac { 3 \times 2 - 1 } { 3 + 2 } \right) = \cot ^ { - 1 } ( 1 ) = \frac { \pi } { 4 } .