0
y=sin x
y=cos x cos x
sin x = cos^2 x
sin x = 1-sin^2 x
sin x -1 + sin^2 x = 0
sin^2 x + sin x -1 = 0
Let y=sin x
y^2+y-1 = 0
This equation is of form ay^2+by+c=0
a = 1 b = 1 c = -1
y=[-b+/-sqrt(b^2-4ac)]/2a]
y=[-1 +/-sqrt(1^2-4(1)(-1)]/(2)(1)
discriminant is b^2-4ac =5
y=[-1 +√(5)] / 2
y=[-1 -√(5)] / 2
sin x = [-1 +√(5)] / 2
x = sin^-1 [-1 +√(5)] / 2] = 0.6662394 radians
x = sin^-1 [-1 -√(5)] / 2] = sin^-1 (-1.618) -- has no solution
When x = 0.6662394 radians, sin x and cos x times cos x are equal.
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