Answer:
see explanation
Step-by-step explanation:
Using the Addition formula for sine
• sin(x + y) = sinxcosy + cosxsiny
and sin120° = sin60°, cos120° = - cos60°
sin240° = - sin60°, cos240°, cos240° = - cos60°
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Consider the left side
Second term
sin(120 + A) = sin120cosA + cos120sinA
= sin60cosA - cos60sinA
Third term
sin(240 + A)
= sin240cosA + cosAsin240
= - sin60cosA - cos60sinA
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Putting the 3 terms together
sinA + sin60cosA - cos60sinA - sin60cosA - cos60sinA
= sinA - 2cos60sinA
= sinA - (2 × [tex]\frac{1}{2}[/tex])sinA
= sinA - sinA
= 0 = right side ⇒ proven
