Question #0ac31

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Answer 1 · 2017-04-07T16:51:14

$L H S = \frac{1 + sin x}{1 - sin x} - \frac{1 - sin x}{1 + sin x}$ $LHS=(1 + sin x) / (1 - sin x) - (1 - sin x) / (1 + sin x)$

$= \frac{{(1 + sin x)}^{2} - {(1 - sin x)}^{2}}{(1 - sin x) (1 + sin x)}$ $=((1 + sin x)^2 - (1 - sin x)^2)/( (1 - sin x) (1 + sin x))$

$= \frac{4 sin x}{1 - {sin}^{2} x}$ $=(4sinx)/ (1 - sin^2 x)$

$= \frac{4 sin x}{{cos}^{2} x}$ $=(4sinx)/ cos^2 x$

$= \frac{2 \cdot 2 sin x cos x}{{cos}^{3} x}$ $=(2*2sinxcosx)/ cos^3 x$

$= 2 \cdot sin (2 x) {sec}^{3} x = R H S$ $=2*sin(2x)sec^3 x=RHS$

proved