Express $7$ $\cos 2x - 2$ $\sin 2x$ in the form of $R \cos(2x + \alpha)$ where \(\alpha

Question

Express $7$ $\cos 2x - 2$ $\sin 2x$ in the form of $R \cos(2x + \alpha)$ where $\alpha$ is in radians. Hence, solve $7$ $\cos 2x - 2$ $\sin 2x = 5$ for $0 \le x \le 2\pi$.

Accepted Answer

(i) $\sqrt{53}\cos(2x+0.278)$ (ii) $x=0.268,\ 2.60,\ 3.41,\ 5.74\text{ rad}$ (3 s.f.)

Trigonometry - Trigonometric Equations

Trigonometry - Trigonometric Equations

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