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

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

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prove 1-sin^2(x/4)=cos(x/2)

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 1

1 - sin^{2} (\frac{1}{4}) = 0.93879 \dots

1 - sin^{2} (\frac{1}{4})

Refine to a decimal form

= 0.93879 \dots

cos (\frac{1}{2}) = 0.87758 \dots

cos (\frac{1}{2})

Refine to a decimal form

= 0.87758 \dots

The two sides are not equal

\Rightarrow False

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cos (0) sin (0) = - sin (0)

3 sin (x^{2}) + 4 cos^{2} (x) = 3 + cos^{2} (x)

\frac{1 - csc ( x )}{sec ( x )} = cot (x) cos (x)