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Question

Prove that
$$\cos A/(1-\sin A)+\cos A/ (1+\sin A)=2\sec A$$


Solution

LHS$$=\dfrac{\cos A}{1-\sin A}+\dfrac{\cos A}{1+\sin A}=\dfrac{\cos A(1+\sin A+1-\sin A)}{(1-\sin^2 A)}=\dfrac{2\cos A}{\cos^2  A}\\=\dfrac{2}{\cos A}\\=2\text{sec} A=RHS$$ 
Hence proved.

Mathematics

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