In the case of trig functions what is inside the parentheses is the angle value the trig function acts upon. cos 30 degrees + cos 60 degrees is not equal to cos (30+60) = cos(90) degrees.
cos pi/4 = .707 and cos pi/6 = .866. Their sum is 1.573.
cos (pi/4 + pi/6) is cos (10pi/24) = .259.
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