What is the simplified value of \frac{\cot A + \tan B}{\cot B + \tan A} ?

SSC CGL 5 Aug 2017 Shift 1 Paper

Question : 69 of 100

Marks: +1, -0

What is the simplified value of

{\cot A + \tan B}/{\cot B + \tan A}

Solution:

{\cot A + \tan B}/{\cot B + \tan A}={{\cos A }/{\sin A}+{\sin B}/{\cos B}}/{{\cos B }/{\sin B}+{\sin A}/{\cos A}}

{{\cos A \cos B + \sin A \sin B}/{\sin A \cos B}}/{{\cos A \cos B + \sin A \sin B}/{\sin B \cos A}}

={\sin B \cos A}/{\sin A \cos B}= \tanB \cot A

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