Q. 23

# If x = a sec θ cos φ, y = b sec θ sin φ and z = c tan θ, then

A.

B.

C.

D.

Answer :

Given: x a sec θ cos ϕ

Squaring both sides, we get

x^{2} = a^{2} sec^{2} θ cos^{2}ϕ

and y = b sec θ sin ϕ

Squaring both sides, we get

y^{2} = b^{2} sec^{2} θ sin^{2}ϕ

And z = c tan θ

⇒ z^{2} = c^{2} tan^{2} θ

………(i)

To find:

Consider

= sec^{2} θ cos^{2}ϕ + sec^{2} θ sin^{2}ϕ

= sec^{2} θ (cos^{2}ϕ + sin^{2}ϕ)

= sec^{2} θ [∵ sin^{2}ϕ + cos^{2}ϕ = 1]

= 1 + tan^{2} θ [∵ 1 + tan^{2} θ = sec^{2} θ]

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