Is (1+cos(2x))/(sin(2x))= 1/(tan(x)) ?

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

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prove (1+cos(2x))/(sin(2x))= 1/(tan(x))

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Manipulating right side

\frac{1}{tan ( x )}

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

cos (2 x) = cos (x + x)

\frac{csc ( a )}{cot ( a ) + tan ( a )} = cos (a)

2 cos (x) sin^{2} (x) = sin (x) sin (2 x)

sec (x) sin (x) = tan (x)

(tan (θ) + cot (θ)) tan (θ) = sec^{2} (θ)

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