Find-solution-set-of-equation-6cos-x-8sin-x-5-3-0-x-360-

Question Number 151941 by john_santu last updated on 24/Aug/21

Find solution set of equation

6 \cos x - 8 \sin x = 5 \sqrt{3}

0 ° ⩽ x ⩽ 360 °

Answered by iloveisrael last updated on 24/Aug/21

\Leftrightarrow 3 \cos x - 4 \sin x = \frac{5 \sqrt{3}}{2}

\Leftrightarrow \frac{3}{5} \cos x - \frac{4}{5} \sin x = \frac{\sqrt{3}}{2}

\Leftrightarrow \sin 143 ° \cos x + \cos 143 ° \sin x = \sin 60 °

\Leftrightarrow \sin (x + 143 °) = \sin 60 °

{\begin{cases} x = - 83 ° + k . 360 °; x = 277 ° \\ x = - 23 ° + k . 360 °; x = 337 ° \end{cases}