Question #def7c

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Answer 1 · 2017-04-11T22:14:13

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

$= \frac{1 - sin x}{cos x} + \frac{cos x (1 + sin x)}{(1 - sin x) (1 + sin x)}$ $=(1-sinx)/cosx+(cosx(1+sinx))/((1-sinx)(1+sinx))$

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

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

$= \frac{1 - sin x}{cos x} + \frac{1 + sin x}{cos x}$ $=(1-sinx)/cosx+(1+sinx)/cosx$

$= \frac{1}{cos x} - \frac{sin x}{cos x} + \frac{1}{cos x} + \frac{sin x}{cos x}$ $=1/cosx-sinx/cosx+1/cosx+sinx/cosx$

$= \frac{2}{cos x} = 2 sec x$ $=2/cosx=2secx$