Is (sin(3x)+sin(5x))/(cos(3x)-cos(5x))=cot(x) ?

The answer to whether (sin(3x)+sin(5x))/(cos(3x)-cos(5x))=cot(x) is True

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prove (sin(3x)+sin(5x))/(cos(3x)-cos(5x))=cot(x)

prove

\frac{sin ( 3 x ) + sin ( 5 x )}{cos ( 3 x ) - cos ( 5 x )} = cot (x)

True

Solution steps

\frac{sin ( 3 x ) + sin ( 5 x )}{cos ( 3 x ) - cos ( 5 x )} = cot (x)

Manipulating left side

\frac{sin ( 3 x ) + sin ( 5 x )}{cos ( 3 x ) - cos ( 5 x )}

Rewrite using trig identities

= \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

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

2 sin (4 (\frac{5 π}{3})) = 3

sin (a) csc (a) = 1

csc (θ) - cot (θ) = \frac{sin ( θ )}{1 - cos ( θ )}

2 csc (2 x) = tan (x) = cot (x)

Is (sin(3x)+sin(5x))/(cos(3x)-cos(5x))=cot(x) ?
The answer to whether (sin(3x)+sin(5x))/(cos(3x)-cos(5x))=cot(x) is True