Is sin(a+b)=sin(a)+sin(b) ?

The answer to whether sin(a+b)=sin(a)+sin(b) is False

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prove sin(a+b)=sin(a)+sin(b)

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

a = 1

For

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

plug in

b = π

sin (1 + π) = - 0.84147 \dots

sin (1 + π)

Refine to a decimal form

= - 0.84147 \dots

sin (1) + sin (π) = 0.84147 \dots

sin (1) + sin (π)

Refine to a decimal form

= 0.84147 \dots

The two sides are not equal

\Rightarrow False

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Is sin(a+b)=sin(a)+sin(b) ?
The answer to whether sin(a+b)=sin(a)+sin(b) is False