Question

Determine the value of a:
2tanx - tan2x + 2a = 1 - (tan2x)(tan^2x)

Answer 1

I have no idea if i did it right but i got: a = (1-tanx)/2

Answer 2

The answer is 1/2

Answer 3

I have no idea how to get the answer tho :(

Answer 4

\[2\tan x-\tan 2x+2a=1-\left( \tan 2x \right)\left( \tan ^2x \right)\]
\[\tan 2x \tan ^2x-\tan 2x+2a+2\tan x-1=0\]
\[\tan 2x \left( \tan ^2x-1 \right)+2a=1- 2\tan x\]
\[\frac{ 2\tan x }{ 1-\tan ^2x }\left\{ -\left( 1-\tan ^2x \right) \right\}+2a=1-2\tan x\]
\[-2\tan x+2a=1-2\tan x\]
a=1/2,
assume \[1-\tan ^2x \neq 0\]