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Q. $ (1-\tan A)\,(\cot \,A+1) $ is equal to

J & K CETJ & K CET 2010Trigonometric Functions

Solution:

$ (1-\tan A)\,(\cot \,A+1) $
$ =\left( 1-\frac{1}{\cot \,A} \right)\,\left( \frac{1}{\tan \,A}+1 \right) $
$ =\left( \frac{\cos \,A-1}{\cot \,A} \right)\,\left( \frac{1+\tan \,A}{\tan \,A} \right) $
$ =(1+\tan \,A)(\cot \,A-1) $