$\begingroup$ Safer to factor: $\cos x(\sin x+1)=0$. A product is zero, so one of the factors must be zero. Two possibilities, either $\cos x=0$ or $\sin x=-1$. The “rule” that you violated, as user2825632 pointed out, was to divide by a potential zero. $\endgroup$ – If $\cos3x=\cos2x\cdot\cos x$ $4\cos^3x-3\cos x=(2\cos^2x-1)\cos x$ $\iff\cos x[4\cos^2x-3-(2\cos^2x-1)]=0$ $\iff\cos x[\sin^2x]=0\iff\cos x=0$ or $\sin x=0\implies\sin2x=0$ $\implies x$ has to be a multiple of $\dfrac\pi2$ So, $\cos3x=\cos2x\cdot\cos x$ is an equation, not an identity Analysis. We must pay attention to the sign in the equation for the general form of a sinusoidal function. The equation shows a minus sign before C. Therefore f ( x) = sin ( x + π 6 ) − 2 can be rewritten as f ( x) = sin ( x − ( − π 6 ) ) − 2. If the value of C is negative, the shift is to the left. Separate fractions. Convert from 1 cos(x) 1 cos ( x) to sec(x) sec ( x). Divide 0 0 by 1 1. Multiply 0 0 by sec(x) sec ( x). Subtract 1 1 from both sides of the equation. Take the inverse tangent of both sides of the equation to extract x x from inside the tangent. Simplify the right side. cos(x^2) Natural Language; Math Input; Extended Keyboard Examples Upload Random. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by cos^4(x) Natural Language; Math Input; Extended Keyboard Examples Upload Random. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by .

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