Is sin(2y)=(2tan(y))/(1+tan^2(y)) ?

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

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prove sin(2y)=(2tan(y))/(1+tan^2(y))

prove

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

True

Solution steps

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

Manipulating right side

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

Express with sin, cos

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

Rewrite using trig identities

= sin (2 y)

We showed that the two sides could take the same form

\Rightarrow True

sec^{2} (β) + sec^{2} (β) = \frac{2}{cos ^{2} ( β )}

3 csc (x) - cot (x) = \frac{3 - cos ( x )}{sin ( x )}

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

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

2 sin (x) = tan (x)

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