If x=r sec α cos β, y=r sec α sin β and z=r tan α, prove that  x2+y2z2=r2 .


Answer:


Step by Step Explanation:
  1. Substituting the values of x, y, and z in x2+y2z2=r2, we have x2+y2z2=r2 sec2 α cos2 β+r2 sec2 α sin2 βr2 tan2 α=r2 sec2 α (cos2 β+sin2 β)r2 tan2 α=r2 sec2 αr2 tan2 α[cos2 β+sin2 β=1]=r2 (sec2 αtan2 α)=r2 (1)[sec2 αtan2 α=1]=r2
  2. Hence, x2+y2z2 = r2 .

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