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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Express with sin, cos

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

Rewrite using trig identities

= sin (2 a)

We showed that the two sides could take the same form

\Rightarrow True

10 sec^{2} (θ) - 4 tan^{2} (θ) = 4 + 6 sec^{2} (θ)

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

sin^{2} (a) - cos^{2} (a) = 1 - 2 cos^{2} (a)

tan (2 A) - 2 tan (2 A) sin^{2} (A) = sin (2 A)

\frac{1}{tan ( x ) csc ( x )} = cos (x)

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