Is (sin(2θ))/(1+cos(2θ))=tan(θ) ?

The answer to whether (sin(2θ))/(1+cos(2θ))=tan(θ) is True

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prove (sin(2θ))/(1+cos(2θ))=tan(θ)

prove

\frac{sin ( 2 θ )}{1 + cos ( 2 θ )} = tan (θ)

True

Solution steps

\frac{sin ( 2 θ )}{1 + cos ( 2 θ )} = tan (θ)

Manipulating left side

\frac{sin ( 2 θ )}{1 + cos ( 2 θ )}

Rewrite using trig identities

= \frac{sin ( θ )}{cos ( θ )}

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

= tan (θ)

We showed that the two sides could take the same form

\Rightarrow True

\frac{sec ( x ) + tan ( x )}{csc ( x ) + 1} = tan (x)

tan (a) = \frac{sec ( a )}{csc ( a )}

sec (x) tan (x) cos (x) cot (x) = 1

1 - sec (x) cos^{3} (x) = sin^{2} (x)

sin (2 x) (1 - cos (2 x)) = 4 sin^{3} (x) cos (x)

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