We write sin x * sin x = sin2 x
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(2 sin^2 x - 1)/(sin x - cos x) = sin x + cos x (sin^2 x + sin^2 x - 1)/(sin x - cos x) =? sin x + cos x [sin^2 x - (1 - sin^2 x)]/(sin x - cos x) =? sin x + cos x (sin^2 x - cos^2 x)/(sin x - cos x) =? sin x + cos x [(sin x - cos x)(sin x + cos x)]/(sin x - cos x) =? sin x + cos x sin x + cos x = sin x + cos x
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.
The differential of sin x with respect to x is: d(sin x) = cos x dx
It isn't. The derivate of sin x = cos x.It isn't. The derivate of sin x = cos x.It isn't. The derivate of sin x = cos x.It isn't. The derivate of sin x = cos x.