The number of solution(s) of `2cos^(2)(x/2)sin^(2)x=x^(2)+1/x^(2), 0 le x le pi//2`, is/ are-

Options

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

Answer

A

Explanation

Let `y=2cos^(2)(x/2)sin^(2)x=x^(2)+1/x^(2) rArr y=(1+cosx)sin^(2)x` and `y=x^(2)+1/x^(2)`
When `y=(1+cosx)sin^(2)x`= (a number `lt 2`) (a number ` le1`) `rArr y lt 2`……………(i)
and when `y=x^(2)+1/x^(2)=(x-1/x)^(2)+2 ge2 rArr y ge 2`………….(ii)
No value of y can be obtained satisfying (i) and (ii), simultaneously
`rArr` No real solution of the equation exits.