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

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

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

prove

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

True

Solution steps

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

Manipulating left side

cos (6 0^{\circ})

Simplify

= \frac{1}{2}

Manipulating right side

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

Simplify

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

= \frac{1}{2}

We showed that the two sides could take the same form

\Rightarrow True

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