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Question: One root of the equation \(3\cos x + 4\sin x = 6\)lies in the interval....

One root of the equation 3cos⁡x+4sin⁡x=63\cos x + 4\sin x = 6lies in the interval.

A

35cos⁡x+45sin⁡x=65\frac{3}{5}\cos x + \frac{4}{5}\sin x = \frac{6}{5}

B

cos⁡(x−θ)=65\cos(x - \theta) = \frac{6}{5}

C

[ \left\lbrack \begin{aligned} & \\ & \end{aligned} \right.\

D

 θ=cos⁡−1(35)]\left. \ \theta = \cos^{- 1}\left( \frac{3}{5} \right) \right\rbrack

Answer

35cos⁡x+45sin⁡x=65\frac{3}{5}\cos x + \frac{4}{5}\sin x = \frac{6}{5}

Explanation

Solution

4π+α4\pi + \alpha, 5π−α5\pi - \alpha

[0,5π]\lbrack 0,5\pi\rbrack, ∴\therefore

∴ One root lies in the interval 3sin⁡x+cos⁡x=4\sqrt{3}\sin x + \cos x = 4.