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

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

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

prove

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

True

Solution steps

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

Manipulating left side

cos (2 u)

Rewrite using trig identities

= cos (u) cos (u) - sin (u) sin (u)

Simplify

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

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

We showed that the two sides could take the same form

\Rightarrow True

(csc (θ) + 1) (csc (θ) - 1) = cot^{2} (θ)

cos (θ) (cot (θ) + tan (θ)) = csc (θ)

sin (- θ) = - sin (θ)

- sin (x) = sin (- x)

sec (θ) cot (θ) sin (θ) = 1

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