If ^@ x^@ = ^@a{\space} cosec{\space} \theta^@ and ^@y^@ = ^@b{ | Math Question and Answer

Answer:

Step by Step Explanation:

We are told that $\begin{aligned} & x = a{\space} cosec{\space} \theta \\ {\implies} & \dfrac {a} {x} = \dfrac { 1 } { cosec {\space} \theta } \\ {\implies} & \dfrac {a} {x} = sin {\space} \theta &&\ldots \text{(i)} \\ \end{aligned}$ Also, $\begin{aligned} & y = b {\space} sec{\space} \theta \\ {\implies} & \dfrac {b} {y} = \dfrac { 1 } { sec {\space} \theta } \\ {\implies} & \dfrac {b} {y} = cos {\space} \theta &&\ldots \text{(ii)} \end{aligned}$
On squaring and adding $\text{(i)}$ and $\text{(ii)}$ , we get $\bigg ( \dfrac { a^2 } { x^2 } + \dfrac { b^2 } { y^2 } \bigg) = sin^2{\space} \theta + cos^2 {\space} \theta = 1$

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