SOLUTION: verify the question sec^2x-csc^2x=(tanx-cotx)/(sinx*cosx)

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Question 433559: verify the question
sec^2x-csc^2x=(tanx-cotx)/(sinx*cosx)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
use these identities:


tan^2x+1 = sec^2x)

1 + cot^2x = csc^2x

prove that left side is equal to right side:
sec^2x-csc^2x=(tan^2x + 1)-(1 +cot^2x

=tan^2 x + 1-1 - cot^2 x
=tan^2x - cot^2x
=(tan x - cotx)(tan x + cotx)..................use identities tanx= sinx/cosx and cotx = cosx/sinx
=(tan x - cotx)(sin x/cos x +cos x/sin x)
=(tan x - cotx)((sin xsin x +cos xcos x)/sin xcos x
=(tan x - cotx)((sin ^2x +cos^2 x)/sin xcos x
=%28tan+x+-+cotx%29%281%2Fsin+xcos+x%29
=%28tan+x+-+cotx%29%2Fsin+xcos+x