Is cos^2(7θ)-sin^2(7θ)=cos(14θ) ?

The answer to whether cos^2(7θ)-sin^2(7θ)=cos(14θ) is True

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prove cos^2(7θ)-sin^2(7θ)=cos(14θ)

prove

cos^{2} (7 θ) - sin^{2} (7 θ) = cos (14 θ)

True

Solution steps

cos^{2} (7 θ) - sin^{2} (7 θ) = cos (14 θ)

Manipulating left side

cos^{2} (7 θ) - sin^{2} (7 θ)

Rewrite using trig identities

cos^{2} (7 θ) - sin^{2} (7 θ)

Use the Double Angle identity:

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

= cos (2 \cdot 7 θ)

Simplify

= cos (14 θ)

= cos (14 θ)

We showed that the two sides could take the same form

\Rightarrow True

Is cos^2(7θ)-sin^2(7θ)=cos(14θ) ?
The answer to whether cos^2(7θ)-sin^2(7θ)=cos(14θ) is True