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

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

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

prove

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

True

Solution steps

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

Manipulating left side

sin (x + x)

Rewrite using trig identities

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)

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)

= 2 sin (x) cos (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1 - sin ^{2} ( β )}{cos ( β )} = cos (β)

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

csc (2 x) - cot (2 x) = tan (2 x)

sin (x) = 1 - cos (x)

\frac{sec ( 2 x ) + 1}{tan ( 2 x )} = cot (x)

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