Is cos(330)=1-2sin^2(165) ?

The answer to whether cos(330)=1-2sin^2(165) is True

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prove cos(330)=1-2sin^2(165)

prove

cos (33 0^{\circ}) = 1 - 2 sin^{2} (16 5^{\circ})

True

Solution steps

cos (33 0^{\circ}) = 1 - 2 sin^{2} (16 5^{\circ})

Manipulating left side

cos (33 0^{\circ})

Simplify

cos (33 0^{\circ}) : \frac{3}{2}

= \frac{3}{2}

Manipulating right side

1 - 2 sin^{2} (16 5^{\circ})

Expand

1 - 2 sin^{2} (16 5^{\circ}) : \frac{3}{2}

= \frac{3}{2}

We showed that the two sides could take the same form

\Rightarrow True

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

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

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

(1 - tan^{2} (θ)) = sec^{2} (θ) - 4 tan^{2} (θ)

sin (x) (sin (2 x)) = sin (3 x)

Is cos(330)=1-2sin^2(165) ?
The answer to whether cos(330)=1-2sin^2(165) is True