Trig1.2

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Show that \frac{1+\sin A-\cos A}{1+\sin A+\cos A}+\frac{1+\sin A+\cos A}{1+\sin A-\cos A}=2\csc A\,

Simplifying the given,

\frac{[(1+\sin A)-\cos A]^2+[(1+\sin A)+\cos A]^2}{[(1+\sin A)+\cos A][(1+\sin A)-\cos A]}\,

\frac{2[(1+\sin A)^2+\cos^2 A]}{[(1+\sin A)^2-\cos^2 A]}\,

\frac{2[1+2\sin A+\sin^2 A+\cos^2 A]}{[1+2\sin A+\sin^2 A-1+\sin^2 A]}\,

\frac{2\cdot2(1+\sin A)}{2\sin A(1+\sin A)}=\frac{2}{\sin A}=2\csc A\, which is equal to RHS.


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