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

1 Answer
Geoff K.
Dec 16, 2016

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

Related questions
See all questions in Proving Identities
Impact of this question
1161 views around the world
You can reuse this answer
Creative Commons License