Is (1+sin(2x))/(sin(2x))=1+1/2 sec(x)csc(x) ?

The answer to whether (1+sin(2x))/(sin(2x))=1+1/2 sec(x)csc(x) is True

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prove (1+sin(2x))/(sin(2x))=1+1/2 sec(x)csc(x)

prove

\frac{1 + sin ( 2 x )}{sin ( 2 x )} = 1 + \frac{1}{2} sec (x) csc (x)

True

Solution steps

\frac{1 + sin ( 2 x )}{sin ( 2 x )} = 1 + \frac{1}{2} sec (x) csc (x)

Manipulating left side

\frac{1 + sin ( 2 x )}{sin ( 2 x )}

Rewrite using trig identities

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

Manipulating right side

1 + \frac{1}{2} sec (x) csc (x)

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{1}{csc ( x ) + 1} + \frac{1}{sin ( x ) + 1} = 1

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

cos (θ) cot (θ) + sin (θ) = csc (θ)

cos (2 u) = cos^{2} (u) - sin^{2} (u)

Is (1+sin(2x))/(sin(2x))=1+1/2 sec(x)csc(x) ?
The answer to whether (1+sin(2x))/(sin(2x))=1+1/2 sec(x)csc(x) is True