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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Express with sin, cos

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

Rewrite using trig identities

= cos (2 v)

We showed that the two sides could take the same form

\Rightarrow True

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

sin (A) = \frac{1}{csc ( A )}

\frac{9}{tan ( x )} + \frac{9}{cot ( x )} = 9 tan (x) + 9 cot (x)

sin (2 x) cos (2 x) = 4 sin (x) cos (x)

2 cos^{2} (x) = 2 cos (x) cos (x)

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