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  4. If tan (x+y)=33 and x= tan -13 , then y will be

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

Jharkhand CECEJharkhand CECE 2011

Solution:

Given, $ \tan (x+y)=33 $
$ \Rightarrow $ $ x+y={{\tan }^{-1}}(33) $
$ \Rightarrow $ $ y={{\tan }^{-1}}(33)-x $
$ [\because \,\,x={{\tan }^{-1}}(3)] $
$ \Rightarrow $ $ y={{\tan }^{-1}}(33)-{{\tan }^{-1}}(3) $ (given)
$ \Rightarrow $ $ y={{\tan }^{-1}}\left( \frac{33-3}{1+33.3} \right)={{\tan }^{-1}}\left( \frac{30}{100} \right) $
$ ={{\tan }^{-1}}(0.3) $