Question

Cos2x=cos^2x-1/2

Answer 1

i think you mean solve \[\cos(2x)=\cos^2(x)-\frac{1}{2}\]

Answer 2

do you want to prove the equality?

Answer 3

first note that \[\cos(2x)=\cos^2(x)-\sin^2(x)\] That means that the equation becomes
\[\cos^2(x)-\sin^2(x) = \cos^2(x)-\frac{1}{2}\]

\[\sin^2(x) = \frac{1}{2}\]

\[\sin(x) = \frac{\sqrt{2}}{2}\]

the principle value is \[x=\frac{\pi}{4}\] however note that sinx must be positive so only angles in quadrants 1 and 2 will work.

So the answer is \[x=\frac{\pi}{4}+2n\pi\]

or \[x=\frac{3\pi}{4}+2n\pi\]

where n is a integer.


because sin(3pi/4) also equals sqrt(2)/2
also note that adding an integer multiple of twopi will not change the answer.

Answer 4

@allism1995 its an invalid expression

Answer 5

no he wants to solve the equation for x

Answer 6

@stylestar5678

Answer 7

ya ik