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

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

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

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 1

For

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

plug in

y = 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

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

sin^{2} (2 θ) = 4 sin^{2} (θ) cos^{2} (θ)

csc (t) + cot (t) = \frac{tan ( t )}{sec ( t ) - 1}

\frac{cos ( 4 x ) + cos ( 6 x )}{sin ( 4 x ) - sin ( 6 x )} = - cot (x)

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

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