Question

(1+tanA+cotA)(sinA-cosA)=?

Answer 1

( 1 + tan A + cot A ) ( sin A - cos A )

$( 1 + \frac{Sin A }{Cos A}+ \frac{Cos A }{Sin A } ) ( Sin A - Cos A ) \\ \\ = ( 1 + \frac{Sin^{2}A + Cos^{2} A}{CosA Sin A} )* ( Sin A - Cos A ) \\ \\ = ( \frac{Cos A Sin A +1 }{Cos A Sin A }) ( Sin A - Cos A ) \\ \\ \\ \\ = \frac{ CosA Sin^{2}A - Cos^{2} A Sin A + Sin A - Cos A }{Cos A Sin A }\\ \\ \\ \\ = Sin A - Cos A + Sec A - Cosec A$