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

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

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

prove

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

True

Solution steps

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

Let:

u = \frac{x}{2}

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

Prove

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

True

Therefore

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

We showed that the two sides could take the same form

\Rightarrow True

\frac{tan ( x ) + cot ( x )}{sec ( x )} = csc (x)

sec^{2} (θ) - 1 = tan^{2} (θ)

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

sin (x) cos (x) (tan (x) + cot (x)) = 1

tan^{2} (x) sec^{2} (x) + sec^{2} (x) = sec^{4} (x)