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How do you prove this trigonometric relationship sin3A equals 3sinA cos 2 A - sin 3 A?
Wiki User
∙ 14y ago
sin(3A) = sin(2A + A) = sin(2A)*cos(A) + cos(2A)*sin(A)= sin(A+A)*cos(A) + cos(A+A)*sin(A)
= 2*sin(A)*cos(A)*cos(A) + {cos^2(A) - sin^2(A)}*sin(A)
= 2*sin(A)*cos^2(A) + sin(a)*cos^2(A) - sin^3(A)
= 3*sin(A)*cos^2(A) - sin^3(A)
Wiki User
∙ 9y ago
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