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

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

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

prove

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

True

Solution steps

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

Manipulating left side

sin (2 x) + sin (2 y)

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

sin (θ) csc (θ) cos (θ) = cos (θ)

cot (x) - csc^{2} (x) cot (x) = - cot^{3} (x)

cot (x - \frac{π}{2}) = - tan (x)

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

cos (4 x) - sin (4 x) = cos (2 x)

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