Is sin(a+b)-sin(a-b)=2cos(a)sin(b) ?

The answer to whether sin(a+b)-sin(a-b)=2cos(a)sin(b) is True

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prove sin(a+b)-sin(a-b)=2cos(a)sin(b)

prove

sin (a + b) - sin (a - b) = 2 cos (a) sin (b)

True

Solution steps

sin (a + b) - sin (a - b) = 2 cos (a) sin (b)

Manipulating right side

2 cos (a) sin (b)

Rewrite using trig identities

= sin (a + b) - sin (a - b)

We showed that the two sides could take the same form

\Rightarrow True

1 + cot^{2} (θ) = \frac{1}{sin ^{2} ( θ )}

sin (2 π - x) = - sin (x)

csc (θ) - \frac{sin ( θ )}{1 + cos ( θ )} = cot (θ)

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

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

Is sin(a+b)-sin(a-b)=2cos(a)sin(b) ?
The answer to whether sin(a+b)-sin(a-b)=2cos(a)sin(b) is True