Show that cotxcosx+tanxsinx=(cosecx+secx)(1-sinxcosx)

=(cosecx+secx)(1-sinxcosx)

=(cosecx+secx)(sin^2x-sinxcosx+cos^2x)

= sinx+ [sin^2x/cosx]-cosx-sinx+[cos^2x/sinx]+co…

= [sin^2x/cosx]+[cos^2x/sinx]

= [sinx/cosx](sinx)+[cosx/sinx](cosx)

= tanxsinx+cotxcosx

Is it acceptable? Thank You.

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