If cos α + cos β + cos γ = 0 = sin α + sin β + sin γ then s i n ( α + β + γ ) s i n 3 α + s i n 3 β + s i n 3 γ is equal to

Question

If cos α + cos β + cos γ = 0 = sin α + sin β + sin γ then s i n ( α + β + γ ) s i n 3 α + s i n 3 β + s i n 3 γ ​ is equal to

TestHub · Accepted Answer

Let a = e i α , b = e i β , c = e iγ clearly a + b + c = 0 ⇒ a 1 ​ + b 1 ​ + c 1 ​ = 0 a + b + c = 0 ⇒ a 3 + b 3 + c 3 = 3 ab c ⇒ sin 3 α + sin 3 β + sin 3 γ = 3 sin ( α + β + γ ) .

Mathematics - Complex Number Question with Solution | TestHub

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