How Sin (A+B) × Sin (A-B) = Sin²A - Sin²B ?
How Sin (A+B) × Sin (A-B) = Sin²A - Sin²B ? ➡ Sin(A+B) = SinA CosB + CosA SinB ➡ Sin(A-B) = SinA CosB - CosA SinB
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How Cos 2θ = (1 - tan²θ)/ (1 + tan²θ) ?
How Cos 2θ = (1 - tan²θ)/ (1 + tan²θ) ? ➡ Cos(2A) = Cos²A - Sin²A
How tan (3A) = (3tanA - tan³A)/(1-3tan²A)?
How tan (3A) = (3tanA - tan³A)/(1-3tan²A)? 👉 How tan(A+B) = (tanA + tanB)/(1- tanA tanB ) ?
How tan (2A) = (2 tan A)/ (1- tan²A) ?
How tan (2A) = (2 tan A)/ 1- tan²A? ➡ How tan(A+B) = (tanA + tanB)/(1- tanA tanB ) ?
How sin 3A = 3SinA - 4Sin³A?
How sin 3A = 3SinA - 4Sin³A? Sin(3A) = Sin(2A +A) As we know that Sin(A+B) = SinA CosB + CosA SinB then, ➡Sin(2A + A) = Sin2A CosA + Cos2A SinA also, { Sin(2A) = 2 SinA CosA } .........(1) { Cos(2A) = Cos²A - Sin²A } ......(2) Put the value of (1) and (2) in formula ➡Sin(2A + A) = (2 SinA CosA)CosA + (Cos²A - Sin²A)SinA also, Cos²A = 1 - Sin²A ➡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