Trigonometric Expression

[flakine]

Verify the identy

2 cos^2x - 1=1-2 sin^2x

Please help.

 

[soroban]

Hello, flakine!

You're expected to know: .\(\displaystyle sin^2x\,+\,\cos^2x\:=\:1\quad\Rightarrow\quad\cos^2x\:=\:1\,-\,\sin^2x\)
. . Then this is one of the easier ones . . .

Verify the identity: .\(\displaystyle 2\cos^2x\,-\,1\:=\:1\,-\,2\sin^2x\)

On the left, we have: . \(\displaystyle 2\cos^2x\,-\,1\)
. . . . . . . . . . . . . . . . . . . . .\(\displaystyle \downarrow\)
Then we have: . . . \(\displaystyle 2(1\,-\,\sin^2x)\,-\,1\:=\:2\,-\,2\sin^2x\,-\,1\;=\;1\,-\,2\sin^2x\) . . . . there!