Prove that identity tan2x - tanx = tanx sec2x

I managed to start i think but am not sure

(2tan x / 1-tan^2 x) - tan x

but i don't know what else

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- Jul 11th 2008, 01:25 AMgraceyIdentities
Prove that identity tan2x - tanx = tanx sec2x

I managed to start i think but am not sure

(2tan x / 1-tan^2 x) - tan x

but i don't know what else - Jul 11th 2008, 01:46 AMkalagota
- Jul 11th 2008, 02:39 AMnikhilHere it is
hi!gracey (sweet name)

your starting is absolutly fine.

(2tan x / 1-tan^2 x) - tan x

now what you should really do is take tanx common

tanx[(2/(1-tan^2x)-1]

now use

tan^2x=(1-cos2x)/1+cos2x

after substituting we get

tanx[2/(1-{(1-cos2x)/1+cos2x})-1]

=tanx[{(1+cos2x)/cos2x}-1]

=tanx[1/cos2x]

=tanxsec2x

hence proved - Jul 11th 2008, 03:53 AMSoroban
Hello, gracey!

A variation of nikhil's solution . . .

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Prove the identity: .

I managed to start i think, but am not sure

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