The number of values of x in `(0, pi)` satisfying the equation
`(sqrt(3) "sin" x + "cos" x) ^(sqrt(sqrt(3)"sin" 2x -"cos" 2x+ 2)) = 4`, is

Options

A. 0
B. 1
C. 2
D. none of these

Answer

B

Explanation

`(sqrt(3) "sin" x + "cos" x) ^(sqrt(sqrt(3)"sin" 2x -"cos" 2x+ 2)) = 4`
`rArr (sqrt(3) "sin" x + "cos" x) ^((sqrt(3)"sin" x +"cos" x)) = 2^(2)`
`[because (sqrt(3)"sin" x + "cos" x)^(2) = sqrt(3) "sin" 2x-"cos"2x + 2]`
`rArr sqrt(3) "sin" x + "cos" x = 2`
`rArr "sin" (x + (pi)/(6)) = 1 rArr x + (pi)/(6) = (pi)/(2) rArr x = (pi)/(3)`
Thus, there is only one solution.