Is cos^2(2θ)-sin^2(2θ)=2cos^2(2θ)-1 ?

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

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prove cos^2(2θ)-sin^2(2θ)=2cos^2(2θ)-1

prove

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

True

Solution steps

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

Manipulating left side

cos^{2} (2 θ) - sin^{2} (2 θ)

Rewrite using trig identities

= 2 cos^{2} (2 θ) - 1

We showed that the two sides could take the same form

\Rightarrow True

csc (x) \cdot cos^{2} (x) + sin (x) = csc (x)

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

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

Is cos^2(2θ)-sin^2(2θ)=2cos^2(2θ)-1 ?
The answer to whether cos^2(2θ)-sin^2(2θ)=2cos^2(2θ)-1 is True