Is cot(s)=((sin(2s)))/((1-cos(2s))) ?

The answer to whether cot(s)=((sin(2s)))/((1-cos(2s))) is True

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prove cot(s)=((sin(2s)))/((1-cos(2s)))

prove

cot (s) = \frac{( sin ( 2 s ) )}{( 1 - cos ( 2 s ) )}

True

Solution steps

cot (s) = \frac{sin ( 2 s )}{1 - cos ( 2 s )}

Manipulating right side

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

Rewrite using trig identities

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

Use the Double Angle identity:

sin (2 x) = 2 sin (x) cos (x)

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

Use the Double Angle identity:

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

= \frac{2 sin ( s ) cos ( s )}{1 - ( 1 - 2 sin ^{2} ( s ) )}

Simplify

\frac{2 sin ( s ) cos ( s )}{1 - ( 1 - 2 sin ^{2} ( s ) )} : \frac{cos ( s )}{sin ( s )}

\frac{2 sin ( s ) cos ( s )}{1 - ( 1 - 2 sin ^{2} ( s ) )}

Expand

1 - (1 - 2 sin^{2} (s)) : 2 sin^{2} (s)

1 - (1 - 2 sin^{2} (s))

- (1 - 2 sin^{2} (s)) : - 1 + 2 sin^{2} (s)

- (1 - 2 sin^{2} (s))

Distribute parentheses

= - (1) - (- 2 sin^{2} (s))

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - 1 + 2 sin^{2} (s)

= 1 - 1 + 2 sin^{2} (s)

1 - 1 = 0

= 2 sin^{2} (s)

= \frac{2 sin ( s ) cos ( s )}{2 sin ^{2} ( s )}

Divide the numbers:

\frac{2}{2} = 1

= \frac{sin ( s ) cos ( s )}{sin ^{2} ( s )}

Cancel the common factor:

sin (s)

= \frac{cos ( s )}{sin ( s )}

= \frac{cos ( s )}{sin ( s )}

= \frac{cos ( s )}{sin ( s )}

Use the basic trigonometric identity:

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

= cot (s)

We showed that the two sides could take the same form

\Rightarrow True

\frac{3 sin ^{2} ( x )}{tan ^{2} ( x )} = 3 cos^{2} (x)

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

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

sec (A) - \frac{cos ( A )}{1 + sin ( A )} = tan (A)

sin (3 a) = 3 sin (a) - sin (a)

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