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

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

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

prove

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

True

Solution steps

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

Let:

u = \frac{x}{2}

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

Prove

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

True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

cos (3 α) = 4 cos^{3} (α) - 3 cos (α)

\frac{1}{sin ( 2 θ )} - \frac{1}{tan ( 2 θ )} = tan (θ)

sin (x) cot (x) + cos (x) tan^{2} (x) = sec (x)

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

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

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