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

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

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

prove

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

True

Solution steps

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

Manipulating left side

1 - cos (2 x)

Rewrite using trig identities

= 2 sin^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{sin ^{2} ( t )}{tan ^{2} ( t )} = cos^{2} (t)

tan (- θ) = - tan (θ)

tan (θ + π) = tan (θ)

cos (\frac{π}{6}) = \frac{3}{2}

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