Question #55104

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Answer 1 · 2017-03-22T10:06:18

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

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

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

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

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

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

$= \frac{2}{sin x} = 2 csc x$ $=2/sinx=2cscx$