The equation 2cos2⁡x2sin2⁡x=x2+1x2,0≤x≤π2 has

Clearly ,  LHS =2cos2⁡(x/2)sin2⁡x≤2 and,  RHS =x2+1x2≥2Thus, the equality holds when each side is equal to 2. But, RHS is equal to 2 for x =1 while LHS is less than 2 for this value of x. Consequently the equation has no solution.