The value of $$4\left[\frac{(1 - \sec A)^{2} + (1 + \sec A)^{2}}{1 + \sec^{2}A}\right]$$ is :
$$4\left[\frac{(1 - \sec A)^{2} + (1 + \sec A)^{2}}{1 + \sec^{2}A}\right]$$
=Â $$4\left[\frac{1 + \sec^{2}AÂ - 2\sec AÂ +Â 1 + \sec^{2}A + 2\sec A}{1 + \sec^{2}A}\right]$$
= $$4\left[\frac{2(1 + \sec^{2}A) }{1 + \sec^{2}A}\right]$$ = 8
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