Is cos(60)=2cos^2(30)-1 ?

The answer to whether cos(60)=2cos^2(30)-1 is True

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prove cos(60)=2cos^2(30)-1

prove

cos (6 0^{\circ}) = 2 cos^{2} (3 0^{\circ}) - 1

True

Solution steps

cos (6 0^{\circ}) = 2 cos^{2} (3 0^{\circ}) - 1

Manipulating left side

cos (6 0^{\circ})

Simplify

= \frac{1}{2}

Manipulating right side

2 cos^{2} (3 0^{\circ}) - 1

Simplify

- 1 + 2 cos^{2} (3 0^{\circ}) : \frac{1}{2}

= \frac{1}{2}

We showed that the two sides could take the same form

\Rightarrow True

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

sec^{2} (θ) = \frac{1}{cos ^{2} ( θ )}

csc^{2} (θ) = \frac{1}{sin ^{2} ( θ )}

sin (x) = \frac{1}{2}

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