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Vadim26 [7]
3 years ago
11

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..​​
Mathematics
2 answers:
stealth61 [152]3 years ago
7 0

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

We have to <u>evaluate</u> the given <u>expression</u>.

\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) } }

<u>We know that:</u>

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

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

Therefore, <u>the expression becomes:</u>

\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)

zmey [24]3 years ago
3 0

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

<em>see </em><em>the </em><em>attachment</em><em>!</em><em>!</em>

hope it helps

#carryolearning

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