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

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

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

prove

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

True

Solution steps

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

Manipulating right 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

sec^{2} (x) csc^{2} (x) = csc^{2} (x) + sec^{2} (x)

cot (π - θ) = - cot (θ)

sec (x) + cos (x) = - sin^{2} (x) sec (x)

\frac{( sec ( x ) - 1 )}{1 - cos ( x )} = sec (x)

sin (x + 2 π) = sin (x)

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