Is (1-cos(2θ))/(sin(2θ))=tan(θ) ?

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

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prove (1-cos(2θ))/(sin(2θ))=tan(θ)

prove

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

True

Solution steps

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

Manipulating left 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

\frac{cos ( 3 x )}{sin ( x )} + \frac{sin ( 3 x )}{cos ( x )} = 2 cot (2 x)

sin (A + B) = sin (A) + sin (B)

\frac{cot ^{2} ( B ) - cos ^{2} ( B )}{csc ^{2} ( B ) - 1} = cos^{2} (B)

cos (2 a) = 1 - 2 sin^{2} (a)

sec^{2} (x) - tan^{2} (x) = tan (x) cot (x)

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