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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Use the basic trigonometric identity:

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

= tan (x)

We showed that the two sides could take the same form

\Rightarrow True

(1 + tan^{2} (x)) cos^{2} (x) = 1

\frac{1 - sin ( θ )}{cos ( θ )} = sec (θ) - tan (θ)

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

tan (\frac{θ}{2}) = \frac{1 - cos ( θ )}{sin ( θ )}

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

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