Is cos(12x)=1-2sin^2(6x) ?

The answer to whether cos(12x)=1-2sin^2(6x) is True

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prove cos(12x)=1-2sin^2(6x)

prove

cos (12 x) = 1 - 2 sin^{2} (6 x)

True

Solution steps

cos (12 x) = 1 - 2 sin^{2} (6 x)

Manipulating right side

1 - 2 sin^{2} (6 x)

Rewrite using trig identities

1 - 2 sin^{2} (6 x)

Use the Double Angle identity:

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

= cos (2 \cdot 6 x)

Simplify

= cos (12 x)

= cos (12 x)

We showed that the two sides could take the same form

\Rightarrow True

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