If x = a cosec θ sin ϕ, y = b cosec θ cos ϕ and z = c cot θ then prove that (x2a2+y2b2)=(1+z2c2).


Answer:


Step by Step Explanation:
  1. We are given that xa=cosec θ sin ϕ(i)yb=cosec θ cos ϕ(ii)zc=cot θ(iii)
  2. On squaring and adding (i) and (ii), we get (x2a2+y2b2)=cosec2 θ(sin2 ϕ+cos2 ϕ)=cosec2 θ[
  3. Hence, \bigg( \dfrac { x^2 } { a^2 } + \dfrac { y^2 } { b^2 } \bigg) = \bf \bigg( 1 + \dfrac { z^2 } { c^2 } \bigg).

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