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

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

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

prove

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

True

Solution steps

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

Manipulating left side

2 cos (x) sin (y)

Rewrite using trig identities

= sin (x + y) - sin (x - y)

We showed that the two sides could take the same form

\Rightarrow True

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

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

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

1 - 4 sin^{2} (x) cos^{2} (x) = cos^{2} (2 x)

sin (3 x) = sin (x) (4 cos^{2} (x) - 1)

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