Prove that $\sec A (1 - \sin A)(\sec A + an A) = 1$.

Question

Prove that $\sec A (1 - \sin A)(\sec A + 	an A) = 1$.

Accepted Answer

Step 1: LHS $= \sec A(1 - \sin A)(\sec A + 	an A) = \frac{1}{\cos A}(1 - \sin A)\left(\frac{1}{\cos A} + \frac{\sin A}{\cos A}ight)$
Step 2: $= \frac{1}{\cos A}(1 - \sin A) \cdot \frac{(1 + \sin A)}{\cos A}$
Step 3: $= \frac{1 - \sin^2 A}{\cos^2 A} = \frac{\cos^2 A}{\cos^2 A} = 1 =$ RHS. Hence proved.

Question

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