Question:
(1 + cot A + tan A) (sin A – cos A) = sin A tan A – cot A cos A
Solution:
$(1+\cot A+\tan A)(\sin A-\cos A)$
$=\sin A+\cot A \sin A+\tan A \sin A-\cos A-\cot A \cos A-\tan A \cos A$
$=\sin A+\frac{\cos A}{\sin A} \times \sin A+\tan A \sin A-\cos A-\cot A \cos A-\frac{\sin A}{\cos A} \times \cos A$
$=\sin A+\cos A+\tan A \sin A-\cos A-\cot A \cos A-\sin A$
$=\sin A \tan A-\cot A \cos A$
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