in trigonometry, when do we substitute a formula, use LCM, multiply it with something ??
eg:root of 1+cosA/1-cosA + root of 1-cosA/1+cosA
sin^4A-cos^$A=1-2cos^2A

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Solution

$\frac{\sqrt{1 + \cos A}}{\sqrt{1 - \cos A}} + \frac{\sqrt{1 - \cos A}}{\sqrt{1 + \cos A}} = \frac{(1 + \cos A) + (1 - \cos A)}{\sqrt{1 - \cos A} \sqrt{1 - \cos A}} = \frac{2}{\sqrt{1 - \cos^{2} A}} [as, 1 - \cos^{2} A = \sin^{2} A] = \frac{2}{\sin A} = 2 cosec A [as, \frac{1}{\sin A} = cosec A]$

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\frac{s i n A + c o s A}{s i n A - c o s A} + \frac{s i n A - c o s A}{s i n A + c o s A} = \frac{2}{1 - 2 c o s^{2} A}

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