Is cos(x)=(sin(2x))/(2sin(x)) ?

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

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prove cos(x)=(sin(2x))/(2sin(x))

prove

cos (x) = \frac{sin ( 2 x )}{2 sin ( x )}

True

Solution steps

cos (x) = \frac{sin ( 2 x )}{2 sin ( x )}

Manipulating right side

\frac{sin ( 2 x )}{2 sin ( x )}

Rewrite using trig identities

\frac{sin ( 2 x )}{2 sin ( x )}

Use the Double Angle identity:

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

= \frac{2 sin ( x ) cos ( x )}{2 sin ( x )}

Simplify

\frac{2 sin ( x ) cos ( x )}{2 sin ( x )} : cos (x)

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

Divide the numbers:

\frac{2}{2} = 1

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

Cancel the common factor:

sin (x)

= cos (x)

= cos (x)

= cos (x)

We showed that the two sides could take the same form

\Rightarrow True

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

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

\frac{cot ( θ ) tan ( θ )}{sec ( θ )} = cos (θ)

sin (a) cos (a) = cos^{2} (a) tan (a)

(cos (x)) (tan (x)) (csc (x)) = 1

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