Trig identities: how does tan2x=2tanx/1-tan^2x become 2tanx and 1-tan^2x?

[ken_165]

Hello! I just want to ask:
The equation says: tan2x=2tanx/1-tan^2x.
How did it become 2tanx and 1-tan^2x?

 

[mmm4444bot]

… The equation says: tan2x = 2 tanx/(1-tan^2x) …

Note the grouping symbols (shown in red). They are required, when texting symbolic ratios containing multiple terms/factors on top or bottom. :idea: For more tips, check out the link in the forum guidelines about how to format math as text.

How did it become 2tanx and 1-tan^2x?

You'll find your answer by googling keywords prove double-a͏͏ngle identity for tangent. There are a variety of approaches. :cool:

 

[Deleted member 4993]

Hello! I just want to ask:
The equation says: tan2x=2tanx/1-tan^2x.
How did it become 2tanx and 1-tan^2x?

You should know:

tan(2*x) = sin(2*x)/cos(2*x)

You should also know:

sin(2*x) = 2 * sin(x) * cos(x)

and

cos(2*x) = [cos(x)]^2 - [sin(x)]^2

continue...