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Question: If \(\tan ( x + y ) = 33\)and \(x = \tan ^ { - 1 } 3\)then y will be....

If tan⁡(x+y)=33\tan ( x + y ) = 33and x=tan⁡−13x = \tan ^ { - 1 } 3then y will be.

A

0.30.3

B

tan⁡−1(1.3)\tan ^ { - 1 } ( 1.3 )

C

tan⁡−1(0.3)\tan ^ { - 1 } ( 0.3 )

D

tan⁡−1(118)\tan ^ { - 1 } \left( \frac { 1 } { 18 } \right)

Answer

tan⁡−1(0.3)\tan ^ { - 1 } ( 0.3 )

Explanation

Solution

x+y=tan⁡−133⇒y=tan⁡−133−tan⁡−13x + y = \tan ^ { - 1 } 33 \Rightarrow y = \tan ^ { - 1 } 33 - \tan ^ { - 1 } 3

=tan⁡−133−31+99=tan⁡−130100= \tan ^ { - 1 } \frac { 33 - 3 } { 1 + 99 } = \tan ^ { - 1 } \frac { 30 } { 100 }⇒ y=tan⁡−1(0.3)y = \tan ^ { - 1 } ( 0.3 ) .