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

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

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

prove

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

True

Solution steps

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

Let:

u = \frac{x}{2}

(cos (u) - sin (u))^{2} = 1 - sin (2 u)

Prove

(cos (u) - sin (u))^{2} = 1 - sin (2 u) :

True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

2 cos^{2} (w) - 1 = 1 - 2 sin^{2} (w)

sin (x) (1 + cot^{2} (x)) = csc^{2} (x)

(1 - cos (x)) (1 + sec (x)) = - sin (x)

4 cot (x) = cot (x) sin^{2} (x)

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

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