Question

Find the value of k:-

cotA/1+cosecA-cotA/1-cosecA=k/cosA​

Answer 1

Step-by-step explanation:

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Answer 2

solution ;

$\frac{ \cot(x) }{1 + \csc(x) } - \frac{ \cot(x) }{1 - \csc(x) } = \frac{k}{ \cos(x) }$

solve LHS;

$\frac{ \cot(x) }{ 1 + \csc(x) } - \frac{ \cot(x) }{ 1 - \csc(x) }$

$= \frac{ \frac{ \cos(x) }{ \sin(x) } }{1 + \frac{1}{ \sin(x) } } - \frac{ \frac{ \cos(x) }{ \sin(x) } }{1 - \frac{1}{ \sin(x) } }$

$= \frac{ \cos(x) }{1 + \sin(x) } - \frac{ \cos(x) }{ \sin(x) - 1 }$

$= \frac{ \cos(x) }{1 + \sin(x) } + \frac{ \cos(x) }{ 1 - \sin(x) }$

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

$= \frac{ \cos(x) - \cos(x) \sin(x) + \cos(x) \sin(x) + \cos(x) }{ \cos {}^{2} ( x ) }$

$= \frac{2}{ \cos(x) }$

so the value of k = 2

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