If x = a . , y = b .sin , z = c tan . then the value of x^2a^2 + y^2b^2 - z^2c^2 is?

Answer: Option A

$$\begin{array}{rl}& x=a\sec \theta .\cos \varphi \\ & y=b\sec \theta .sin\varphi \\ & z=c\text{ tan}\theta \\ & \frac{x}{a}=\sec \theta .\cos \varphi \\ & \frac{y}{b}=\sec \theta .sin\varphi \\ & \frac{z}{c}=\text{tan}\theta \\ & \therefore \frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}\\ & \Rightarrow {\sec }^2\theta .{\cos }^2\varphi +{\sec }^2\theta .si{n}^2\varphi -\text{ta}{\text{n}}^2\theta \\ & \Rightarrow {\sec }^2\theta \left({\cos }^2\varphi +si{n}^2\varphi \right)-\text{ta}{\text{n}}^2\theta \\ & \Rightarrow {\sec }^2\theta -\text{ta}{\text{n}}^2\theta \\ & \Rightarrow 1\end{array}$$