Is cos(2u)=2cos^2(u)-1 ?

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

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prove cos(2u)=2cos^2(u)-1

prove

cos (2 u) = 2 cos^{2} (u) - 1

True

Solution steps

cos (2 u) = 2 cos^{2} (u) - 1

Manipulating left side

cos (2 u)

Rewrite using trig identities

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

Use the Pythagorean identity:

cos^{2} (u) + sin^{2} (u) = 1

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

= cos^{2} (u) - (1 - cos^{2} (u))

Simplify

cos^{2} (u) - (1 - cos^{2} (u)) : 2 cos^{2} (u) - 1

= 2 cos^{2} (u) - 1

We showed that the two sides could take the same form

\Rightarrow True

tan (2 x) (1 - tan^{2} (x)) = 2 tan (x)

csc (x) - cos (x) \cdot cot (x) = sin (x)

sin (x) \cdot csc (x) = 1

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

csc^{2} (θ) (1 - cos^{2} (θ)) = sin (648 0^{\circ})