Prove that $\sec A(1-\sin A)(\sec A+\tan A)=1$
Prove that $\sec A(1-\sin A)(\sec A+\tan A)=1$
$LHS =\sec A (1-\sin A )(\sec A +\tan A )$
$=\left(\frac{1}{\cos A }\right)(1-\sin A )\left(\frac{1}{\cos A }+\frac{\sin A }{\cos A }\right)$
$=\frac{(1-\sin A)(1+\sin A)}{\cos ^{2} A}=\frac{1-\sin ^{2} A}{\cos ^{2} A}$
$=\frac{\cos ^{2} A}{\cos ^{2} A}=1=R H S$
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