Question

E2%80%8B%7D%7D%20%5C%5C%20" id="TexFormula1" title="Evaluate: \sqrt{ \frac {1 - sin(x)}{1 + sin(x)​​}} \\ " alt="Evaluate: \sqrt{ \frac {1 - sin(x)}{1 + sin(x)​​}} \\ " align="absmiddle" class="latex-formula">
Solve this problem please..​​

Answer 1

$\large\underline{\sf{Solution-}}$

We have to evaluate the given expression.

$\rm = \sqrt{ \dfrac{1 - \sin(x) }{1 + \sin(x) } }$

If we multiple both numerator and denominator by 1 - sin(x), then the value remains same. Let's do that.

$\rm = \sqrt{ \dfrac{[1 - \sin(x)][1 - \sin(x) ]}{[1 + \sin(x)][1 - \sin(x) ]} }$

$\rm = \sqrt{ \dfrac{[1 - \sin(x)]^{2}}{1- \sin^{2} (x) } }$

We know that:

$\rm \longmapsto { \sin}^{2}(x) + \cos^{2}(x) = 1$

$\rm \longmapsto \cos^{2}(x) = 1 - { \sin}^{2}(x)$

Therefore, the expression becomes:

$\rm = \sqrt{ \dfrac{[1 - \sin(x)]^{2}}{\cos^{2} (x)}}$

$\rm = \dfrac{1 - \sin(x)}{\cos(x)}$

$\rm = \dfrac{1}{\cos(x)} - \dfrac{ \sin(x) }{ \cos(x) }$

$\rm = \sec(x) - \tan(x)$

Answer 2

$\sqrt{ \frac{ \cos(n) }{1 + \: \sin(n) } }$

see the attachment!!

hope it helps

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