Question

if cosecA +cotA=5 then find the value of cosA​

Answer 1

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Answer 2

Given : $cosec\ A+\cot A=5$

To find : $\cos A=?$

Solution:

$cosec\ A+\cot A=5$

and

$cosec\ A-\cot A=\dfrac{1}{5}$

So, On adding both the terms we get :

$2cosec\ A=5+\dfrac{1}{5}=\dfrac{25+1}{5}=\dfrac{26}{5}\\\\cosec\ A=\dfrac{26}{5\times 2}=\dfrac{13}{5}$

So, the value of sin would be :

$\sin A=\dfrac{5}{13}\\\\So, \\\\\cos A=\sqrt{1-sin^2 A}=\sqrt{1-(\dfrac{5}{13})^2}=\sqrt{\dfrac{169-25}{169}}=\sqrt{\dfrac{144}{169}}=\dfrac{12}{13}$

Hence, the value of cos A is $\dfrac{12}{13}$