I need to prove that the following is true. Thanks
(2tanx /1-tan^x)+(1/2cos^2x-1)= (cosx+sinx)/(cosx - sinx)
and thanks ...........

check your typing.
I tried 30º, the two sides are not equal, they differ by 1

oh , thank you Mr Reiny I'll tell my teacher this Question is Wrong .

not necessarily.

look at your first term
what does tan^x mean?

I want you to check what you typed here with your question.

Mr Reiny ,
I tried 30º, the two sides are equal

Yes, if the term at the bottom is tan^2 x,
you typed tan^x, and I read it as tan x

I got the proof, give me a bit of time to type it

I'm sorry Mr Reiny you are right it is tan^2x .

2tanx/(1-tan^2x) + 1/(2cos^2x -1)
= 2sinx/cosx [1/(1-sin^2x/cos^2x)] + 1/(2cos^2x -(sin^2x + cos^2x))
=2sinx/cosx [cos2x/(cos^2x - sin^2x)] + 1/(cos^2x - sin^2x) reduce to get same denominator
=2sinxcosx/(cos^2x-sin^2x) + 1/(cos^2x-sin^2x)
=(2sinxcosx + sin^2x + cos^2x)/(cos^2x-sin^2x)
= (cosx+sinx)(cosx+sinx)/[cosx+sinx)(cosx-sinx)]
=(cosx+sinx)/(cosx - sinx)
= Right Side!!!!!

thank you Mr Reiny

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