How do you prove # cscx-(secxsin^2x)/tanx=cos^3xcscxsecx #?

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Answer 1 · 2016-05-19T09:42:05

Please see below.

#cscx-(secxsin^2x)/tanx#

= #1/sinx-(1/cosx xxsin^2x)/(sinx/cosx)#

= #1/sinx-(1/cosx xxsin^2x xx cosx/sinx)#

= #1/sinx-sinx#

= #(1-sin^2x)/sinx#

= #cos^2x/sinx#

= #cos^2xcscx xx cosx xx1/cosx#

= #cos^2x xx cscx xx cosx xx secx#

= #cos^3xcscxsecx#