sin4A=sinA+sin2A
sin ( 2(2A)) = sin A + sin 2A
2sin2Acos2A = sinA + sin2A
2sin2A ( 1 - 2sin^2A) = sinA + sin2A
2sin2A - 4sin2A(sin^2A) = sinA + sin2A
sin(2A) - 4sin(2A)* (sin^2( A)) = sin(A)
2sinAcosA - 8sinAcosA (sin^2A) = sinA
sinA [ 2cosA - 8cosA (1 -cos^2A) ] - 1 = 0
sinA = 0 A = 0”
2cosA - 8cosA (1 -cos^2 A) = 1
2cosA - 8cosA + 8cos^3A - 1 = 0
8cos^3 A - 6cosA - 1 = 0
Let A = x
8x^3 - 6x - 1 = 0
Using WolframAlpha to solve this cubic gives x ≈ .93969
cos A =.93969
arccos (.93969) = A = 20°
