Is cos(2θ)=(csc^2(θ)-2)/(csc^2(θ)) ?

The answer to whether cos(2θ)=(csc^2(θ)-2)/(csc^2(θ)) is True

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prove cos(2θ)=(csc^2(θ)-2)/(csc^2(θ))

prove

cos (2 θ) = \frac{csc ^{2} ( θ ) - 2}{csc ^{2} ( θ )}

True

Solution steps

cos (2 θ) = \frac{csc ^{2} ( θ ) - 2}{csc ^{2} ( θ )}

Manipulating right side

\frac{csc ^{2} ( θ ) - 2}{csc ^{2} ( θ )}

Express with sin, cos

= 1 - 2 sin^{2} (θ)

Rewrite using trig identities

= cos (2 θ)

We showed that the two sides could take the same form

\Rightarrow True

tan (a) = \frac{1}{cot ( a )}

cos^{4} (x) + sin^{4} (x) = 1

tan^{2} (x) csc^{2} (x) = 1 + tan^{2} (x)

sin (x) = - sin (- x)

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

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