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

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

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

prove

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

True

Solution steps

2 cos (x) sin (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

\frac{cot ( x ) \cdot sec ( x )}{csc ( x )} = 1

sin (x) + tan (x) = tan (x) (1 + cos (x))

3 sin (x) cos (x) = 3 sin^{2} (x) cot (x)

sin (\frac{3 π}{2} - 0) = - cos (0)

sin (x) + cos (2 x) = 4 sin^{2} (x) - 1