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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

cot^{2} (α) = cos^{2} (α) + (cot (α) cos (α))^{2}

cos^{4} (β) - sin^{4} (β) = 2 cos^{2} (β) - 1

(1 - sin^{2} (x)) \cdot csc^{2} (x) = cot^{2} (x)

sec^{2} (x) (1 - cos^{2} (x)) = tan^{2} (x)

cot^{2} (θ) - cos^{2} (θ) = cot^{2} (θ) cos^{2} (θ)

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