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

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

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

prove

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

True

Solution steps

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

Manipulating left 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{csc ^{2} ( x )}{cot ( x )} = csc (x) sec (x)

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

csc (x) - cot (x) cos (x) = sin (x)

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

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