Is 2sin(2x)=4sin(x)cos(x) ?

The answer to whether 2sin(2x)=4sin(x)cos(x) is True

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prove 2sin(2x)=4sin(x)cos(x)

prove

2 sin (2 x) = 4 sin (x) cos (x)

True

Solution steps

2 sin (2 x) = 4 sin (x) cos (x)

Manipulating left side

2 sin (2 x)

Rewrite using trig identities

2 sin (2 x)

Use the Double Angle identity:

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

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

Simplify

= 4 sin (x) cos (x)

= 4 sin (x) cos (x)

We showed that the two sides could take the same form

\Rightarrow True

(sin (x)) (csc (x) - sin (x)) = cos^{2} (x)

tan (x) + cot (x) - sec (x) csc (x) = 0

\frac{1 - sin ( x )}{sec ( x )} = \frac{cos ^{3} ( x )}{1 + sin ( x )}

(1 + cos (θ)) (csc (θ) - cot (θ)) = sin (θ)

cos (2 α) = - 1 + \frac{2}{1 + tan ^{2} ( α )}

Is 2sin(2x)=4sin(x)cos(x) ?
The answer to whether 2sin(2x)=4sin(x)cos(x) is True