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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Simplify

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

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

Divide the numbers:

\frac{2}{2} = 1

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

Cancel the common factor:

sin (2 θ)

= cos (θ)

= cos (θ)

We showed that the two sides could take the same form

\Rightarrow True

- sin (2 x) + cos (2 x) = 1

sin (x) (sec (x) tan (x)) = tan^{2} (x)

sin ((3 θ + 72)^{\circ}) = cos (4 8^{\circ})

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

cot^{2} (x) + csc^{2} (x) = 1 + cot^{2} (x)

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