Question

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2cos120°-x sin120°. cos180°= x tan150°

Answer 1

(2√3 )/5is he value of x.thank you.

Answer 2

`2cos120°-x sin120°. cos180°= x tan150° \\ 2( - (1)/(2) ) - x( ( √(3) )/(2) ) * ( - 1) = x{( \sin( 150°))/( \cos(150°))} \\ ( - (2)/(2) ) - ( √(3) )/(2)x * ( - 1) = x ( (1)/(2) )/( - ( √(3) )/(2) ) \\ - 1 - ( - ( √(3) )/(2)x) = x( (1)/(2) * ( - (2)/( √(3) ) )) \\ - 1 + ( √(3) )/(2) x = ( - (2)/(2 √(3) ) )x \\ - 1 + ( √(3) )/(2) x = ( - (1)/( √(3) ) )x \\ - 1 + ( √(3) )/(2) x =( ( √(3) )/( √(3) ) )( - (1)/( √(3) ) )x \\ - 1 + ( √(3) )/(2) x = - ( √(3) )/(3) x \\ 6( - 1 + ( √(3) )/(2) x) = 6( - ( √(3) )/(3) x) \\ - 6 + (6 √(3) )/(2) x = - (6 √(3) )/(3) x \\ - 6 = ( - 6 √(3) )/(3)x - (6 √(3) )/(2) x \\ - 6 = (- 2 √(3))x - (3 √(3))x \\ - 6 = - 5 √(3) x \\ x = ( - 6)/( - 5 √(3) ) \\ x = ( 6)/(5 √(3) ) \\ x = (6)/(5 √(3) ) * ( √(3) )/( √(3) ) \\ x = (6 √(3) )/(5 * 3) \\ x = (2√(3) )/(5)`