Is cos^2(2u)-sin^2(2u)=cos(4u) ?

The answer to whether cos^2(2u)-sin^2(2u)=cos(4u) is True

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prove cos^2(2u)-sin^2(2u)=cos(4u)

prove

cos^{2} (2 u) - sin^{2} (2 u) = cos (4 u)

True

Solution steps

cos^{2} (2 u) - sin^{2} (2 u) = cos (4 u)

Manipulating left side

cos^{2} (2 u) - sin^{2} (2 u)

Rewrite using trig identities

cos^{2} (2 u) - sin^{2} (2 u)

Use the Double Angle identity:

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

= cos (2 \cdot 2 u)

Simplify

= cos (4 u)

= cos (4 u)

We showed that the two sides could take the same form

\Rightarrow True

Is cos^2(2u)-sin^2(2u)=cos(4u) ?
The answer to whether cos^2(2u)-sin^2(2u)=cos(4u) is True