The number of points P(x,y) lying inside or on the circle x2+y2=9 and satisfying the equation tan4⁡x+cot4⁡x+2=4sin2⁡y  is

We have tan4⁡x+cot4⁡x+2=4sin2⁡yor  (tan2⁡x−cot2⁡x)2+4=4sin2⁡yNow, LHS ≥ 4 and RHS ≤ 4. Therefore,tan2⁡x=1 and sin2⁡y=1 or tan⁡x=±1 and sin⁡y=±1but, −3≤x≤3 and −3≤y≤3Therefore, the acceptable values of x are ±π4and ±3π4. Theacceptable values of y are ±π2Hence, the number of points p(x,y) are 8