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

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Answer 1 · 2016-03-05T11:57:56

#RHS=cotx#

RHS:

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

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

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

#(cancelsinx-sin^2x+1-cancelsinx)/(sinxcosx)#

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

#(cancel(cos^2x)^cosx)/(sinxcancelcosx)#

#cosx/sinx#

#cotx#=#LHS#

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