Is cos^2(2x)=((1+cos(4x)))/2 ?

The answer to whether cos^2(2x)=((1+cos(4x)))/2 is True

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prove cos^2(2x)=((1+cos(4x)))/2

prove

cos^{2} (2 x) = \frac{( 1 + cos ( 4 x ) )}{2}

True

Solution steps

cos^{2} (2 x) = \frac{1 + cos ( 4 x )}{2}

Manipulating right side

\frac{1 + cos ( 4 x )}{2}

Rewrite using trig identities

\frac{1 + cos ( 4 x )}{2}

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

Use the Double Angle identity:

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

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

Simplify

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

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

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

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

Group like terms

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

1 - 1 = 0

= 2 cos^{2} (2 x)

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

Divide the numbers:

\frac{2}{2} = 1

= cos^{2} (2 x)

= cos^{2} (2 x)

= cos^{2} (2 x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1 + sin ( x )}{cos ( x ) tan ( x ) - 1} = - 1

\frac{sin ( x ) sec ( x )}{tan ( x )} = 1

cot (x) + 5 = 5 + csc (x) \cdot cos (x)

csc (θ) = cos (θ) cot (θ) + sin^{2} (θ) csc (θ)

cos (y) csc (y) = cot (y)

Is cos^2(2x)=((1+cos(4x)))/2 ?
The answer to whether cos^2(2x)=((1+cos(4x)))/2 is True