19. if 2sinA/1+cosA+sinA=y then prove that 1-cosA+sinA/1+sinA is also y

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\frac{sin A + 1 - cos A}{sin A - 1 + cos A} = \frac{1 + sin A}{cos A}

\frac{1 + cos A + sin A}{1 + cos A - sin A} = \frac{1 + sinA}{cos A}

If sinA + 2cosA = 1. Prove that 2sinA -cosA= 2.

\frac{s i n A + c o s A}{s i n A - c o s A} + \frac{s i n A - c o s A}{s i n A + c o s A} = \frac{2}{s i n^{2} A - c o s^{2} A} = \frac{2}{2 s i n^{2} A - 1} = \frac{2}{1 - 2 c o s^{2} A}

\frac{1 + c o s A}{s i n A} + \frac{s i n A}{1 + c o s A} = 2 c o s e c A

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