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

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