Trigonometry Practice Test 1

Question : 37 of 40

Marks: +1, -0

If x = a(1 + cos θ cos ϕ) y = a(1 + cos θ cos ϕ) and z = c (1 + sin θ),then which one of the following is correct?

Solution:

Given that x = a(1 + cos θ cos ϕ) y = a(1 + cos θ cos ϕ) and z = c (1 + sin θ)
Since,

({x-a}/a)^2+({y-b}/b)^2+({z-c}/c)^2

=({a\cosθ\cosϕ}/a)^2+({b\cosθ\sinϕ}/b)^2+({c\sinθ}/c)^2

=\cos^2θ(\cos^2ϕ+\sin^2ϕ)+\sin^2θ

=\cos^2θ+\sin^2θ=1

∴({x-a}/a)^2+({y-b}/b)^2+({z-c}/c)^2=1

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