If x-a -cos- y-b -sin- and z-c tan - show that x 222-y 2 b 2-z 2 c 2-1 -

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Trigonometric Ratios of Allied Angles

If x=a θcosϕ,...

Question

If x = a sec θ cos ϕ, y = b sec θ sin ϕ and z = c tan θ, show that $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} - \frac{z^{2}}{c^{2}} = 1$ .

Open in App

Solution

Suggest Corrections

Similar questions

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}}

\frac{z^{2}}{c^{2}}

1 - \frac{z^{2}}{c^{2}}

\frac{z^{2}}{c^{2}} - 1

1 + \frac{z^{2}}{c^{2}}

(\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}}) = ?

(1 + \frac{z^{2}}{c^{2}})

(1 - \frac{z^{2}}{c^{2}})

(\frac{z^{2}}{c^{2}} - 1)

\frac{z^{2}}{c^{2}}

x = a sec θ cos ϕ, y = b sec θ sin ϕ

z = c tan θ

(\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}}) = (1 + \frac{z^{2}}{c^{2}})

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} - \frac{z^{2}}{c^{2}} = 1, \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} + \frac{z^{2}}{c^{2}} = 1, - \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} + \frac{z^{2}}{c^{2}} = 1 has

θ = {tan}^{- 1} \sqrt{x} + {tan}^{- 1} \sqrt{y} + {tan}^{- 1} \sqrt{z}

x = \frac{a^{2} (a + b + c)}{a b c}, y = \frac{b^{2} (a + b + c)}{a b c}, z = \frac{c^{2} (a + b + c)}{a b c}

tan θ = 0.

Join BYJU'S Learning Program