sin(A + B):
sin A = cos(pi/2 - A)
sin (A + B) = cos(pi/2 - (A + B))
sin(A + B) = cos ((pi/2 - A) - B)
sin(A + B) = cos(pi/2 - A)cosB + sin(pi/2 - A)sinB
sin(A + B) = sinAcosB + cosAsinB
cos(A + B):
(1)
√((cos(A+B) - 1)^2 + (sin(A+B) - 0)^2) = √((cos B - cos A)^2 + (sin B- (-sinA))^2)
(2)
cos^2(A+B) - 2cos(A+B) + 1 + sin^2(A+B)
= cos^2B - 2cosAcosB + cos^2A + sin^2B + 2sinAsinB +sin^2A
2 - 2cos(A+B) = 2 - 2cosAcosB + 2sinAsinB
cos(A + B) = cosAcosB - sinAsinB
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