Question #d92c6

1 Answer
Sep 22, 2017

Proving the identity will not fit in the answer, so look below.

Explanation:

So, we are trying to prove this: tanx-cscxsecx(1-2cos^2x)=cotx
Using this proof: sin^2 x + cos^2x=1...
tanx-cscxsecx(sin^2x+cos^2x-2cos^2x)=cotx
tanx-cscxsecx(sin^2x-cos^2x)=cotx

Using these proofs: tanx = sinx/cosx, cscx=1/sinx and secx=1/cosx.
sinx/cosx-1/(sinxcosx)(sin^2x-cos^2x)=cotx
sinx/cosx-(sin^2x-cos^2x)/(sinxcosx)=cotx

Make both denominators the same on the left side only... (we leave the right side alone for proofs).
(sin^2x-(sin^2x-cos^2x))/(sinxcosx)=cotx
(sin^2x-sin^2x+cos^2x)/(sinxcosx)=cotx
(cos^2x)/(sinxcosx)=cotx
(cosx)/(sinx)=cotx

Use this proof: cosx/sinx = cotx
cotx=cotx