Number of solution `(s)` of the equation `((2-cos^2x)/(sinx))^3+((3-cos2x)/(sinx))=0` is

Options

A. 0
B. 1
C. 2
D. infinite

Answer

A

Explanation

We have,
`((2-"cos"^(2)x)/("sin"x))^(3) + ((3-"cos"2x)/("sin"x)) = 0`
`rArr ((1+"cos"^(2)x)/("sin"x))^(3) + 2((1+"sin"^(2)x)/("sin"x)) = 0`
`rArr ("sin" x + (1)/("sin"x))^(3) + 2("sin"x + (1)/("sin"x)) = 0`
`rArr ("sin"x + (1)/("sin"x)){("sin"x + (1)/("sin"x))^(2) + 2} = 0`
But, `"sin" x + (1)/("sin"x)ge 2 "or" le -2`
So, the given equation has no solution.