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

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

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

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 0

For

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

plug in

y = 1

sin (0 + 1) sin (0 - 1) = - 0.70807 \dots

sin (0 + 1) sin (0 - 1)

Refine to a decimal form

= - 0.70807 \dots

sin (2 \cdot 0) - sin (2 \cdot 1) = - 0.90929 \dots

sin (2 \cdot 0) - sin (2 \cdot 1)

Refine to a decimal form

= - 0.90929 \dots

The two sides are not equal

\Rightarrow False

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