Is 1/(sin(2θ))-1/(tan(2θ))=tan(θ) ?

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

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prove 1/(sin(2θ))-1/(tan(2θ))=tan(θ)

prove

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

True

Solution steps

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

Manipulating left side

\frac{1}{sin ( 2 θ )} - \frac{1}{tan ( 2 θ )}

Express with sin, cos

= \frac{1 - cos ( 2 θ )}{sin ( 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

sin (x) cot (x) + cos (x) tan^{2} (x) = sec (x)

(cot^{2} (x) + 1) (1 - cos^{2} (x)) = 1

sin (x) csc (x) - sin^{2} (x) = cos^{2} (x)

tan (2 π + θ) = tan (θ)

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

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