Is (sin(θ)+sin(3θ))/(2cos(θ))=sin(2θ) ?

The answer to whether (sin(θ)+sin(3θ))/(2cos(θ))=sin(2θ) is True

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prove (sin(θ)+sin(3θ))/(2cos(θ))=sin(2θ)

prove

\frac{sin ( θ ) + sin ( 3 θ )}{2 cos ( θ )} = sin (2 θ)

True

Solution steps

\frac{sin ( θ ) + sin ( 3 θ )}{2 cos ( θ )} = sin (2 θ)

Manipulating left side

\frac{sin ( θ ) + sin ( 3 θ )}{2 cos ( θ )}

Rewrite using trig identities

= sin (2 θ)

We showed that the two sides could take the same form

\Rightarrow True

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

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

\frac{1 + tan ( u )}{1 + cot ( u )} = tan (u)

sec^{2} (B) = \frac{1}{1 - sin ^{2} ( B )}

3 sin^{2} (2 x) = 12 cos^{2} (x) sin^{2} (x)

Is (sin(θ)+sin(3θ))/(2cos(θ))=sin(2θ) ?
The answer to whether (sin(θ)+sin(3θ))/(2cos(θ))=sin(2θ) is True