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Question: The value of \(\cos \left( \tan ^ { - 1 } ( \tan 2 ) \right)\) is....

The value of cos⁡(tan⁡−1(tan⁡2))\cos \left( \tan ^ { - 1 } ( \tan 2 ) \right) is.

A

15\frac { 1 } { \sqrt { 5 } }

B

−15- \frac { 1 } { \sqrt { 5 } }

C

cos⁡2\cos 2

D

−cos⁡2- \cos 2

Answer

cos⁡2\cos 2

Explanation

Solution

cos⁡[tan⁡−1(tan⁡2)]=cos⁡2\cos \left[ \tan ^ { - 1 } ( \tan 2 ) \right] = \cos 2.