# How do you verify sqrt((1-sinx)/(1+sinx))=(1-sinx)/abs(cosx)?

How do you verify sqrt((1-sinx)/(1+sinx))=(1-sinx)/abs(cosx)?

ReportAnswer 1

$\sqrt{\frac{1 - \sin x}{1 + \sin x}} = \frac{1 - \sin x}{|} \cos x |$

#### Explanation:

$\sqrt{\frac{1 - \sin x}{1 + \sin x}}$

= $\sqrt{\frac{1 - \sin x}{1 + \sin x} \times \frac{1 - \sin x}{1 - \sin x}}$

= $\sqrt{{\left(1 - \sin x\right)}^{2} / \left(1 - {\sin}^{2} x\right)}$

= $\sqrt{{\left(1 - \sin x\right)}^{2} / {\cos}^{2} x}$

= $\frac{1 - \sin x}{|} \cos x |$

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