Is 1/2 2sin(x)cos(x)= 1/2 sin(2x) ?

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

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prove 1/2 2sin(x)cos(x)= 1/2 sin(2x)

prove

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

True

Solution steps

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

Manipulating left side

\frac{1}{2} 2 sin (x) cos (x)

Rewrite using trig identities

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

Use the Double Angle identity:

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

1 - tan^{2} (x) = sec^{2} (x)

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

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

\frac{tan ( a )}{sec ( a )} = tan (a) cos (a)

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

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