If x = a secα cosβ, y = b secα sinβ,

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If x = a secα cosβ, y = b secα sinβ, z = c tan α, then the value of
x² +
y² -
z² is
a² b² c²

x = a secα . cosβ

⇒	x	= secα . cosβ
	α

Similarly,

		y	= secα . sinβ,	z	= tanα
		b		c

∴		x²	+	y²	-	z²
		a²		b²		c²

= sec²α. cos²β + sec²α . sin²β – tan²α
= sec²α (cos²β + sin²β) – tan²α
= sec²α – tan²α = 1