Is (1-cos(2u))/(sin(u))=2sin(u) ?

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

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prove (1-cos(2u))/(sin(u))=2sin(u)

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Use the Double Angle identity:

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

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

Simplify

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

\frac{1 - ( 1 - 2 sin ^{2} ( u ) )}{sin ( u )}

Expand

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

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

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

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

Distribute parentheses

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

Apply minus-plus rules

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

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

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

1 - 1 = 0

= 2 sin^{2} (u)

= \frac{2 sin ^{2} ( u )}{sin ( u )}

Cancel the common factor:

sin (u)

= 2 sin (u)

= 2 sin (u)

= 2 sin (u)

We showed that the two sides could take the same form

\Rightarrow True

tan^{2} (θ) = sin^{2} (θ) sec^{2} (θ)

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

tan (6 x) sec (3 x) = 2 sin (3 x) sec (6 x)

sec (θ) (cos (θ) + cot (θ)) = csc (θ)

cos (θ) = \frac{11}{6}

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