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

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

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

prove

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

True

Solution steps

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

Let:

u = \frac{x}{2}

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

Prove

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

True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

sec (x) - cos (x) = sin (x) (tan (x))

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

sec (\frac{π}{2} - t) = csc (t)

csc (x) sec (x) = tan (x) + cot (x)

sin (3 u) = sin (u) (3 - 4 sin^{2} (u))