Is (2sin(x)cos(x))/(2sin^2(x))=cot(x) ?

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

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prove (2sin(x)cos(x))/(2sin^2(x))=cot(x)

prove

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

True

Solution steps

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

Manipulating left side

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

Simplify

\frac{2 cos ( x ) sin ( x )}{2 sin ^{2} ( x )} : \frac{cos ( x )}{sin ( x )}

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

Use the basic trigonometric identity:

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

= cot (x)

We showed that the two sides could take the same form

\Rightarrow True

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

1 + tan^{2} (y) = sec^{2} (y)

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

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

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

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