Is (5sin(2x))/2 = 5/2 (2sin(x)cos(x)) ?

The answer to whether (5sin(2x))/2 = 5/2 (2sin(x)cos(x)) is True

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prove (5sin(2x))/2 = 5/2 (2sin(x)cos(x))

prove

\frac{5 sin ( 2 x )}{2} = \frac{5}{2} (2 sin (x) cos (x))

True

Solution steps

\frac{5 sin ( 2 x )}{2} = \frac{5}{2} \cdot 2 sin (x) cos (x)

Manipulating right side

\frac{5}{2} 2 sin (x) cos (x)

Rewrite using trig identities

\frac{5}{2} \cdot 2 sin (x) cos (x)

= \frac{5}{2} \cdot 1 \cdot 2 sin (x) cos (x)

Use the Double Angle identity:

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

= \frac{5}{2} \cdot 1 \cdot sin (2 x)

Simplify

= \frac{5}{2} sin (2 x)

= \frac{5}{2} sin (2 x)

= \frac{5 sin ( 2 x )}{2}

We showed that the two sides could take the same form

\Rightarrow True

\frac{sin ( 2 θ ) + sin ( θ )}{cos ( 2 θ ) + cos ( θ ) + 1} = tan (θ)

1 + (tan (a))^{2} = 1 + tan^{2} (a)

sec (\frac{x}{2}) = \frac{1}{cos ( \frac{x}{2} )}

1 - sin (x) = cot (x)

4 cos^{2} (θ) + 4 sin^{2} (θ) = 4

Is (5sin(2x))/2 = 5/2 (2sin(x)cos(x)) ?
The answer to whether (5sin(2x))/2 = 5/2 (2sin(x)cos(x)) is True