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

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

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

prove

2 \cdot cos (x) \cdot 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

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

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

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

tan (θ) cos (θ) - sin^{2} (θ) = cos^{2} (θ)

\frac{cot ^{2} ( θ )}{cos ^{2} ( θ )} = csc^{2} (θ)

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