Is cot(θ)=(1+cos(2θ))/(sin(2θ)) ?

The answer to whether cot(θ)=(1+cos(2θ))/(sin(2θ)) is True

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prove cot(θ)=(1+cos(2θ))/(sin(2θ))

prove

cot (θ) = \frac{1 + cos ( 2 θ )}{sin ( 2 θ )}

True

Solution steps

cot (θ) = \frac{1 + cos ( 2 θ )}{sin ( 2 θ )}

Manipulating right side

\frac{1 + cos ( 2 θ )}{sin ( 2 θ )}

Rewrite using trig identities

= \frac{cos ( θ )}{sin ( θ )}

Use the basic trigonometric identity:

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

= cot (θ)

We showed that the two sides could take the same form

\Rightarrow True

cos (\frac{1}{sin ( b )}) \frac{sin ( b )}{cos ( b )} = 1

csc (x) + cot (x) = cot (\frac{x}{2})

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

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

3 sin (9 π - x) = 3 sin (x)

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