Simplify $(cotx)/(cscx-sinx)$ ?

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Answer 1 · 2017-02-24T07:21:53

$(cotx)/(cscx-sinx)=secx$

$(cotx)/(cscx-sinx)$

= $(cosx/sinx)/(1/sinx-sinx)$

= $(cosx/sinx)/((1-sin^2x)/sinx)$

= $(cosx/sinx)/(cos^2x/sinx)$

= $cosx/sinx xxsinx/cos^2x$

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

= $1/cosx$

= $secx$

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