Question

Prove:
\[\huge \frac{2\tan x}{1 + \tan^2 z} = \sin (2x)\]

Answer 1

you could memorize 1+tan^2 identity
or you could change tan to sin/cos
and 1 to cos^2/cos^2 and add, simplify
use the double angle formula
or
sin(a+b)= sin(a)cos(b)+ sin(b)cos(a)
for a=b this becomes 2 sin(a)cos(a)

Answer 2

\[Sin(2x) = 2sinxcosx\]

Answer 3

\[2sinxcosx=\frac{2sinxcosx }{ \cos^2x+\sin^2x }\]

Answer 4

nw Divide Numerator and numerator by cos^2x

Answer 5

\[=\frac{ 2tanx }{ 1+\tan^2x }\]

hence proved...)

Answer 6

that's x not z...darn this lag

Answer 7

@phi is it possible to substitute sec^2 x?

Answer 8

yes, there is more than one way to do this