Question

how do you solve x for cosec(x)-sin(x)=cos(x).cot(3x-50)

Answer 1

SOLUTION

TO SOLVE

cosec x - sin x = cos x cot ( 3x - 50 )

EVALUATION

cosec x - sin x = cos x cot ( 3x - 50 )

$\displaystyle \sf{ \implies \: \frac{1}{ \sin x} - \sin x = \cos x \cot (3x - 50)}$

$\displaystyle \sf{ \implies \: \frac{1 - { \sin}^{2}x }{ \sin x} = \cos x \cot (3x - 50)}$

$\displaystyle \sf{ \implies \: \frac{ { \cos}^{2}x }{ \sin x \: \cos x } = \cot (3x - 50)}$

$\displaystyle \sf{ \implies \: \frac{ { \cos}^{}x }{ \sin x } = \cot (3x - 50)}$

$\displaystyle \sf{ \implies \: \cot x= \cot (3x - 50)}$

$\displaystyle \sf{ \implies \: x= (3x - 50)}$

$\displaystyle \sf{ \implies \: 2 x= 50}$

$\displaystyle \sf{ \implies \: x= 25}$

FINAL ANSWER

Hence the required value of x = 25

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