The values of x between 0 and 2π which satisfy the equation sin⁡x8cos2⁡x=1 are in A.P. The common  difference of the  A.P. is

From the given equation we have 2sin⁡x|cos⁡x|=1/2⇒sin⁡2x=1/2  if cos⁡x>0 and sin⁡2x=−1/2 if cos⁡x<0∴ when cos⁡x>0,sin⁡2x=1/2⇒x=π/8,3π/8when cos⁡x<0,sin⁡2x=−1/2⇒x=5π/8,7π/8. so the required values of x areπ/8,3π/8,5π/8,7π/8which form an A.P. with common difference π/4.