Is 2/(sin(2x))= 1/(sin(x)cos(x)) ?

The answer to whether 2/(sin(2x))= 1/(sin(x)cos(x)) is True

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prove 2/(sin(2x))= 1/(sin(x)cos(x))

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Use the Double Angle identity:

sin (2 x) = 2 sin (x) cos (x)

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

Divide the numbers:

\frac{2}{2} = 1

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

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

We showed that the two sides could take the same form

\Rightarrow True

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

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

sin (x) + cos (x) = 2

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

sin (x + x) = 2 sin (x) cos (x)

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