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

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

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

prove

2 sin (x) \cdot cos (x) = sin (2 x)

True

Solution steps

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

Manipulating right side

sin (2 x)

Rewrite using trig identities

sin (2 x)

Rewrite as

= sin (x + x)

Use the Angle Sum identity:

sin (s + s) = sin (s) cos (s) + cos (s) sin (s)

= sin (x) cos (x) + cos (x) sin (x)

= sin (x) cos (x) + cos (x) sin (x)

Simplify

sin (x) cos (x) + cos (x) sin (x) : 2 sin (x) cos (x)

sin (x) cos (x) + cos (x) sin (x)

Add similar elements:

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

= 2 sin (x) cos (x)

= 2 sin (x) cos (x)

We showed that the two sides could take the same form

\Rightarrow True

cos^{2} (2 t) = (cos (2 t))^{2}

5 \cdot 2 = 5 + 5

- cot (x) + sec (x) csc (x) = tan (x)

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

\frac{cos ( b )}{sin ( b )} = \frac{1}{tan ( b )}

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