How do you prove #(1 + csc x)(sec x - tan x) = cot x#?

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Answer 1 · 2016-08-15T14:00:23

#LHS=(1+cscx)(secx-tanx)#

#=(1+1/sinx)(1/cosx-sinx/cosx)#

#=((sinx+1)/sinx)((1-sinx)/cosx)#

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

#=cos^2x/(sinxcosx)#

#=cosx/sinx=cotx=RHS#

proved