Is cot(2x)=(sec(x)+csc(x))/(2sin(x)-2cos(x)) ?

The answer to whether cot(2x)=(sec(x)+csc(x))/(2sin(x)-2cos(x)) is False

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prove cot(2x)=(sec(x)+csc(x))/(2sin(x)-2cos(x))

prove

cot (2 x) = \frac{sec ( x ) + csc ( x )}{2 sin ( x ) - 2 cos ( x )}

False

Solution steps

cot (2 x) = \frac{sec ( x ) + csc ( x )}{2 sin ( x ) - 2 cos ( x )}

Show that the two sides are not equal

For

cot (2 x) = \frac{sec ( x ) + csc ( x )}{2 sin ( x ) - 2 cos ( x )}

plug in

x = 1

cot (2 \cdot 1) = - 0.45765 \dots

cot (2 \cdot 1)

Refine to a decimal form

= - 0.45765 \dots

\frac{sec ( 1 ) + csc ( 1 )}{2 sin ( 1 ) - 2 cos ( 1 )} = 5.04569 \dots

\frac{sec ( 1 ) + csc ( 1 )}{2 sin ( 1 ) - 2 cos ( 1 )}

Refine to a decimal form

= 5.04569 \dots

The two sides are not equal

\Rightarrow False

Is cot(2x)=(sec(x)+csc(x))/(2sin(x)-2cos(x)) ?
The answer to whether cot(2x)=(sec(x)+csc(x))/(2sin(x)-2cos(x)) is False