Is cos^2(x)=cos^2(x/2)-sin^2(x/2) ?

The answer to whether cos^2(x)=cos^2(x/2)-sin^2(x/2) is False

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prove cos^2(x)=cos^2(x/2)-sin^2(x/2)

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 1

cos^{2} (1) = 0.29192 \dots

cos^{2} (1)

Refine to a decimal form

= 0.29192 \dots

cos^{2} (\frac{1}{2}) - sin^{2} (\frac{1}{2}) = 0.54030 \dots

cos^{2} (\frac{1}{2}) - sin^{2} (\frac{1}{2})

Refine to a decimal form

= 0.54030 \dots

The two sides are not equal

\Rightarrow False

\frac{cos ( b )}{sin ( b )} = \frac{1}{tan ( b )}

\frac{cos ( θ ) csc ( θ )}{cot ^{2} ( θ )} = tan (θ)

cos (\frac{3 π}{2}) = cos (\frac{π}{2})

csc (\frac{π}{2} - x) cos (x) = sec (x) cos (x)

1 + 0 + 1 = - 2 cos (0) + 4

Is cos^2(x)=cos^2(x/2)-sin^2(x/2) ?
The answer to whether cos^2(x)=cos^2(x/2)-sin^2(x/2) is False