Hello, yasaminG!
Prove:
.(secx−tanx)2=1+sinx1−sinx
The left side is:
.\(\displaystyle \L\left(\frac{1}{\cos x}\,-\,\frac{\sin x}{\cos x}\right)^2\;=\;\left(\frac{1\,-\,\sin x}{\cos x}\right)^2\;=\;\frac{(1\,-\,\sin x)^2}{\cos^2x}\)
. . . \(\displaystyle \L\frac{(1\,-\,\sin x)(1\,-\,\sin x)}{1\,-\,\sin^2x}\:=\:\frac{(1\,-\,\sin x)(1\,-\,\sin x)}{(1\,-\,\sin x)(1\,+\,\sin x)} \:=\:\frac{1\,-\,\sin x}{1\,+\,\sin x}\)
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