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