Question

cos2x=-2cos^2x

Answer 1

\(\large\color{blue}{ \displaystyle \cos(2x)=-2\cos^2x }\)

use the double angle identity for cos(2x),

i.e. \(\large\color{blue}{ \displaystyle \cos(2x)~~~\Rightarrow ~~\cos^2(x)-\sin^2(x)}\)

Answer 2

this identity can also be written as (and this will help you more)
\(\large\color{blue}{ \displaystyle \cos(2x)=2\cos^2(x)-1 }\)

Answer 3

(( this is obtained, when you make sin^2x = 1-cos^2x.

this way:

cos^2x - sin^2x
cos^2x - (1 - cos^2x)
cos^2x - 1 + cos^2x
2cos^2x -1 ))

Answer 4

ergo

\(\large\color{blue}{ \displaystyle \cos(2x)=-2\cos^2(x) \\[0.7em] }\)
\(\large\color{blue}{ \displaystyle2\cos^2(x)-1=-2\cos^2(x)\\[0.7em] }\)
\(\large\color{blue}{ \displaystyle4\cos^2(x)=1 \\[0.7em]}\)
\(\large\color{blue}{ \displaystyle(2\cos x)^2=(1)^2 \\[0.7em]}\)

square root both sides, and finish....