How can you show tan^2 x(1+cos2x)=2sin^2xtan2x(1+cos2x)=2sin2x?

1 Answer
Dec 16, 2016

We can use the color(blue)"double angle identity for cos(2x)"double angle identity for cos(2x) as well as the color(green)"ratio identity for tan x"ratio identity for tan x.

Explanation:

tan^2 x (1+color(blue)(cos 2x))= tan^2 x (cancel 1 + color(blue)(2cos^2 x - cancel 1))
color(white)(tan^2 x (1+cos 2x))= tan^2 x (2 cos^2 x)
color(white)(tan^2 x (1+cos 2x))= 2color(green)(tan^2 x) cos^2 x
color(white)(tan^2 x (1+cos 2x))= 2color(green)((sin^2 x / cancel(cos^2 x))) cancel(cos^2 x)
color(white)(tan^2 x (1+cos 2x))= 2 sin^2 x