If sinx+sin2x+sin3x=1, then cos6x−4cos4x+8cos2x= - Infinity Learn Detailed Solution Given that sin x + sin 2 x + sin 3 x = 1 sin x + sin 3 x = cos 2 x Squaring on both sides sin 2 x + sin 6 x + 2 sin 4 x = cos 4 x (1 − cos 2 x) + (1 − cos 2 x) 3 + 2 (1 − cos 2 x) 2 = cos 4 x 1 − cos 2 x + 1 − cos 6 x − 3 cos 2 x + 3 cos 4 x + 2 (1 + cos 4 x − 2 cos 2 x) = cos 4 x 4 − cos 6 x + 4 cos 4 x − 8
Sin3x = sinx Solve for x. - Physics Forums There is a much simpler method to solve problems like that where k is integer (zero included) Maybe you already know this, but just in case, sin [m * pi] = 0 for all m So, x=m*pi for all m satisfies the (trivial) equation: edit: where m is an integer