Is cos^2(4x)= 1/2+1/2 cos(16x) ?

The answer to whether cos^2(4x)= 1/2+1/2 cos(16x) is False

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prove cos^2(4x)= 1/2+1/2 cos(16x)

prove

cos^{2} (4 x) = \frac{1}{2} + \frac{1}{2} cos (16 x)

False

Solution steps

cos^{2} (4 x) = \frac{1}{2} + \frac{1}{2} cos (16 x)

Show that the two sides are not equal

For

cos^{2} (4 x) = \frac{1}{2} + \frac{1}{2} cos (16 x)

plug in

x = 1

cos^{2} (4 \cdot 1) = 0.42724 \dots

cos^{2} (4 \cdot 1)

Refine to a decimal form

= 0.42724 \dots

\frac{1}{2} + \frac{1}{2} cos (16 \cdot 1) = 0.02117 \dots

\frac{1}{2} + \frac{1}{2} cos (16 \cdot 1)

Refine to a decimal form

= 0.02117 \dots

The two sides are not equal

\Rightarrow False

\frac{( sec ^{2} ( t ) )}{sec ^{2} ( t ) - 1} = csc^{2} (t)

sin^{2} (x) = cos (2 x) + 2

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

sin (\frac{3 π}{2} + 0) = - cos (0)

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

Is cos^2(4x)= 1/2+1/2 cos(16x) ?
The answer to whether cos^2(4x)= 1/2+1/2 cos(16x) is False