Simplify $\frac{cot x}{csc x - sin x}$ $(cotx)/(cscx-sinx)$ ?

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Answer 1 · 2017-02-24T07:21:53

$\frac{cot x}{csc x - sin x} = sec x$ $(cotx)/(cscx-sinx)=secx$

$\frac{cot x}{csc x - sin x}$ $(cotx)/(cscx-sinx)$

= $\frac{\frac{cos x}{sin x}}{\frac{1}{sin x} - sin x}$ $(cosx/sinx)/(1/sinx-sinx)$

= $\frac{\frac{cos x}{sin x}}{\frac{1 - {sin}^{2} x}{sin x}}$ $(cosx/sinx)/((1-sin^2x)/sinx)$

= $\frac{\frac{cos x}{sin x}}{\frac{{cos}^{2} x}{sin x}}$ $(cosx/sinx)/(cos^2x/sinx)$

= $\frac{cos x}{sin x} \times \frac{sin x}{{cos}^{2} x}$ $cosx/sinx xxsinx/cos^2x$

= $cancelcosx/cancelsinx xxcancelsinx/(cosx xx cancelcosx$

= $1/cosx$

= $secx$

Simplify (cotx)/(cscx-sinx)cotxcscx−sinx(cotx)/(cscx-sinx)?