Is sin(2α)=(2tan(α))/(1+tan^2(α)) ?

The answer to whether sin(2α)=(2tan(α))/(1+tan^2(α)) is True

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prove sin(2α)=(2tan(α))/(1+tan^2(α))

prove

sin (2 α) = \frac{2 tan ( α )}{1 + tan ^{2} ( α )}

True

Solution steps

sin (2 α) = \frac{2 tan ( α )}{1 + tan ^{2} ( α )}

Manipulating right side

\frac{2 tan ( α )}{1 + tan ^{2} ( α )}

Express with sin, cos

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

Rewrite using trig identities

= sin (2 α)

We showed that the two sides could take the same form

\Rightarrow True

\frac{sec ( θ ) cot ( θ )}{csc ( θ )} = 1

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

\frac{1}{sin ( θ ) cos ( θ )} = sec (θ) csc (θ)

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

sec (x) \frac{tan ( x )}{sin ( x )} = sec^{2} (x)

Is sin(2α)=(2tan(α))/(1+tan^2(α)) ?
The answer to whether sin(2α)=(2tan(α))/(1+tan^2(α)) is True