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(B) The statement $\sin (A+B) = \sin A + \sin B$ is false.To justify this,let us take $A = 30^{\circ}$ and $B = 60^{\circ}$.Left Hand Side $(LHS)$: $\

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False

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(B) The statement $\sin (A+B) = \sin A + \sin B$ is false.To justify this,let us take $A = 30^{\circ}$ and $B = 60^{\circ}$.Left Hand Side $(LHS)$: $\sin (A+B) = \sin (30^{\circ} + 60^{\circ}) = \sin 90^{\circ} = 1$.Right Hand Side $(RHS)$: $\sin A + \sin B = \sin 30^{\circ} + \sin 60^{\circ} = \frac{1}{2} + \frac{\sqrt{3}}{2} = \frac{1+\sqrt{3}}{2}$.Since $1 
eq \frac{1+\sqrt{3}}{2}$,the statement is false.

State whether the following is true or false. Justify your answer.
$\sin (A+B) = \sin A + \sin B$

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State whether the following is true or false. Justify your answer.$\sin (A+B) = \sin A + \sin B$