Question

Find the solution of $\sqrt{3}\cos x-\sin x=1$

Answer 1

Find general solution of $\sqrt{3}cosx-sinx=1$

$\to$ both side divide by 2.

$\frac{\sqrt{3}}{2}cosx-\frac{1}{2}sinx=\frac{1}{2}$

$sin{60}^{\circ }.cosx-sinx.cos{60}^{\circ }=\frac{1}{2}$

$sin(60-x)=\frac{1}{2}$

$sin(60-x)=sin{30}^{\circ }$

$\therefore 60-x={30}^{\circ }$

$\therefore x=60-30$

$\therefore x={30}^{\circ }$