Is tan(θ)=(1-cos(2θ))/(sin(2θ)) ?

The answer to whether tan(θ)=(1-cos(2θ))/(sin(2θ)) is True

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prove tan(θ)=(1-cos(2θ))/(sin(2θ))

prove

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

True

Solution steps

tan (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{sin ( θ )}{cos ( θ )}

Use the basic trigonometric identity:

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

= tan (θ)

We showed that the two sides could take the same form

\Rightarrow True

cos^{2} (x) = sin^{2} (x) cos^{2} (x) + cos^{4} (x)

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

csc (2 θ) + cot (2 θ) = cot (θ)

- tan (x) cos (x) = sin (- x)

sin (x - \frac{3 π}{2}) = cos (x)

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