If sqrt3 cos x − sin x = 1, then general value of x is ______.

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KollegeApply · Accepted Answer

If sqrt3cos x − sin x = 1, then general value of x is `bbunderline(2npi +- pi/3 - pi/6)`. Explanation: Divide the entire equation sqrt3cos x − sin x = 1 by 2, `sqrt3/2 cos x − $\frac{1}{2}$ sin x = $\frac{1}{2}$ Substitute cos (pi/6) = sqrt3/2 and sin (pi/6) = $\frac{1}{2}$ cosx cos(pi/6) - sinx sin(pi/6) = $\frac{1}{2}$` Using the identity cos(A + B) = cosA cosB − sinA sin B cos(x + pi/6) = $\frac{1}{2}$ The general solution for cos $\theta$ = cos $\alpha$ is $\theta$ = 2n$\pi$ $\pm$ $\alpha$. Since cos(pi/3) = $\frac{1}{2}$ x + pi/6 = 2npi $\pm$ pi/3 Subtract pi/6 from both sides to get your exact statement: x = 2npi $\pm$ pi/3 - pi/6

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