Question

19) Find the value of x from 2cot120-xsin 120°cos180°= tan 150°.​

Answer 1

[2cot 120°] - [x (sin 120°)(cos 180°)] = tan 150°

=> [2 cot (180° - 60°)] - [x (sin(180° - 120°))(cos(270° - 90°))] = tan (90° + 60°)

=> [2 (-cot 60°)] - [x (sin 60°) (-sin 90°)] = (-cot 60°)

=> x sin 60° sin 90° - 2 cot 60° = -cot 60°

=> x sin 60° sin 90° = 2 cot 60° - cot 60°

$x( \frac{\sqrt{3} }{2})(1) = \frac{1}{ \sqrt{3} }$

$x = \frac{1}{ \sqrt{3} } \times \frac{2}{ \sqrt{3} }$

$x = \frac{2}{3}$