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The equation 2cos^2(x/2)sin^2x=x^2+x^(-2...

The equation `2cos^2(x/2)sin^2x=x^2+x^(-2);0 <= x <=pi/2` has

A

no real solutions

B

one real solutions

C

more than one real solution

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
A
Given equation is `2cos^(2)((x)/(2))sin^(2) x = x^(2) + x^(-2), x le (pi)/(9)`
LHS `= 2 cos ^(2)((x)/(2))sin^(2) x lt 2` and RHS `= x^(2) + (1)/(x^(2)) ge 2`
`therefore` The equaiton has no real solution.
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