Question

If sec X=13/12 find sin X 
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Answer 1

Answer:-

Given,

$\sf \sec(x) = \frac{13}{12}$

Then,

$\sf \cos(x) = \frac{1}{ \sec(x) } = \frac{12}{13}$

Now,

we know that,

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

So,

$\sf \sin(x) = \sqrt{1 - { \cos}^{2} (x)}$

$\sf = \sqrt{1 - (\frac{12}{13}) ^{2} }$

$\sf = \sqrt{1 - (\frac{144}{169}) }$

$\sf = \sqrt{ (\frac{169 - 144}{169}) }$

$\sf = \sqrt{ (\frac{25}{169}) }$

$\sf = \frac{5}{13}$

Hence,

$\boxed{ \sf \large\sin(x) = \frac{5}{13} }$