Is prove-cos(2θ)=(tan^2(θ)-1)/(1+tan^2(θ)) ?

The answer to whether prove-cos(2θ)=(tan^2(θ)-1)/(1+tan^2(θ)) is True

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prove-cos(2θ)=(tan^2(θ)-1)/(1+tan^2(θ))

prove

- cos (2 θ) = \frac{tan ^{2} ( θ ) - 1}{1 + tan ^{2} ( θ )}

True

Solution steps

- cos (2 θ) = \frac{tan ^{2} ( θ ) - 1}{1 + tan ^{2} ( θ )}

Manipulating right side

\frac{tan ^{2} ( θ ) - 1}{1 + tan ^{2} ( θ )}

Express with sin, cos

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

Rewrite using trig identities

= - cos (2 θ)

We showed that the two sides could take the same form

\Rightarrow True

2 cos^{2} (\frac{x}{2}) - cos (x) = 1

\frac{tan ( x ) + cot ( x )}{sec ( x )} = csc (x)

sec^{2} (θ) - 1 = tan^{2} (θ)

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

sin (x) cos (x) (tan (x) + cot (x)) = 1

Is prove-cos(2θ)=(tan^2(θ)-1)/(1+tan^2(θ)) ?
The answer to whether prove-cos(2θ)=(tan^2(θ)-1)/(1+tan^2(θ)) is True