Question

The value of √3cot20° - 4cos20° is equal to

पर्याय

• 1

• -1

• 0

• \[\frac{1}{2}\]

Answer 1

1

Explanation:

\[\sqrt{3}\cot20^\circ-4\cos20^\circ\]

\[=\sqrt{3}\frac{\cos20^\circ}{\sin20^\circ}-4\cos20^\circ\]

\[=\frac{\sqrt{3}\cos20^{\circ}-4\sin20^{\circ}\cos20^{\circ}}{\sin20^{\circ}}\]

\[=\frac{\frac{2\sqrt{3}}{2}\mathrm{cos}20^\circ-2\mathrm{sin}40^\circ}{\sin20^\circ}\]

\[=\frac{2\sin60^\circ\cos20^\circ-2\sin40^\circ}{\sin20^\circ}\]

\[=\frac{\sin80^\circ+\sin40^\circ-2\sin40^\circ}{\sin20^\circ}\]

\[=\frac{\sin80^\circ-\sin40^\circ}{\sin20^\circ}\]

\[=\frac{2\cos60^\circ\sin20^\circ}{\sin20^\circ}\]

\[=2\times\frac{1}{2}\]

= 1