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. Given: x a sec θ cos ϕ

Squaring both sides, we get

x2 = a2 sec2 θ cos2ϕ

and y = b sec θ sin ϕ

Squaring both sides, we get

y2 = b2 sec2 θ sin2ϕ

And z = c tan θ

z2 = c2 tan2 θ ………(i)

To find: Consider = sec2 θ cos2ϕ + sec2 θ sin2ϕ

= sec2 θ (cos2ϕ + sin2ϕ)

= sec2 θ [ sin2ϕ + cos2ϕ = 1]

= 1 + tan2 θ [ 1 + tan2 θ = sec2 θ] Rate this question :

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