Question

prove that cos 2x =2 cos ²x-1​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

$\cos 2x = 2 \cos ^{2}x - 1$

Step-by-step explanation:

Formula used:-

Let us consider the addition formula,

$cos(x+y)=cosx \cdot cosy-sinx\cdot siny$

Let us equate, X and Y, i.e. X = Y

So, the above formula for $cos 2X$, becomes

$\cos 2X = \cos \left ( X+X \right ) = \cos X \cos X -\sin X \sin X\\ \\ \cos 2X = \cos ^{2}X -\sin ^{2}X----(1)$

We know that,

$sin^2\theta+ cos^2\theta=1\\ \\ sin^2\theta=1-cos^2\theta----(2)$

putting equation (2) in equation (1) we get,

$\cos 2X = \cos ^{2}X - \sin ^{2}X\\ \\ =\cos 2X = \cos ^{2}X-(1-cos^2x)\\ \\ cos2x=2cos^2x-1$