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

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

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

prove

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

True

Solution steps

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

Manipulating right side

2 sin (y) cos (x)

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

sec^{2} (x) tan (x) = \frac{1}{2} sin (2 x)

sin (2 a) = 2 cos (a) sin (a)

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

\frac{sec ( θ ) cot ( θ )}{csc ( θ )} = 1

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

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