How sin 3A = 3SinA - 4Sin³A?

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How sin 3A = 3SinA - 4Sin³A?

Sin(3A) = Sin(2A +A)
As we know that

then, 
➡Sin(2A + A) = Sin2A CosA + Cos2A SinA
also,

Put the value of (1) and (2) in formula
➡Sin(2A + A) = (2 SinA CosA)CosA + (Cos²A - Sin²A)SinA

➡Sin(2A + A) = 2 SinA Cos²A + (Cos²A - Sin²A)SinA

➡Sin(2A + A) = 2 SinA (1- Sin²A) + (1- Sin²A -Sin²A) SinA

➡Sin(2A + A) = 2 SinA (1- Sin²A) + (1- 2Sin²A) SinA

➡Sin(2A + A)= 2 SinA - 2Sin³A + SinA - 2Sin³A

➡ Hence, Sin(2A + A)= 3SinA - 4Sin³A



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