Is (cos(2x)+1)/2 =cos^2(x) ?

The answer to whether (cos(2x)+1)/2 =cos^2(x) is True

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prove (cos(2x)+1)/2 =cos^2(x)

prove

\frac{cos ( 2 x ) + 1}{2} = cos^{2} (x)

True

Solution steps

\frac{cos ( 2 x ) + 1}{2} = cos^{2} (x)

Manipulating left side

\frac{cos ( 2 x ) + 1}{2}

Rewrite using trig identities

\frac{cos ( 2 x ) + 1}{2}

Use the Double Angle identity:

cos (2 x) = 2 cos^{2} (x) - 1

= \frac{2 cos ^{2} ( x ) - 1 + 1}{2}

Simplify

\frac{2 cos ^{2} ( x ) - 1 + 1}{2} : cos^{2} (x)

\frac{2 cos ^{2} ( x ) - 1 + 1}{2}

- 1 + 1 = 0

= \frac{2 cos ^{2} ( x )}{2}

Divide the numbers:

\frac{2}{2} = 1

= cos^{2} (x)

= cos^{2} (x)

= cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

Is (cos(2x)+1)/2 =cos^2(x) ?
The answer to whether (cos(2x)+1)/2 =cos^2(x) is True