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

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

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

prove

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

True

Solution steps

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

Let:

u = \frac{x}{2}

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

Prove

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

True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

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

csc (x) = sin (x)

- cos (x) = sin (x + \frac{π}{2})

\frac{cos ( x ) \cdot sec ( x )}{tan ( x )} = cot (x)

81 - 9 (3 sin (x))^{2} = 12 sec (x)

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