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

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

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

prove

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

True

Solution steps

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

Manipulating right side

csc (2 x)

Express with sin, cos

csc (2 x)

Use the basic trigonometric identity:

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

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

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

Rewrite using trig identities

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

Use the Double Angle identity:

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

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

cos (x + \frac{π}{2}) = sin (x)

\frac{sec ( x ) - cos ( x )}{cos ( x )} = tan^{2} (x)

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

tan (\frac{π}{2} - x) sin (x) = cos (x)

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

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