Question

Eliminate $\theta$, if

$x=3cosec\theta +4cot\theta ,y=4cosec\theta -3cot\theta$
Answer: $(3x+4y{)}^2-(4x-3y{)}^2=625$
If true then enter 1 else if False enter 0

Answer 1

$x=3cosec\theta +4cot\theta$ (1)
$y=4cosec\theta -3cot\theta$ (2)
Multiply equation (1) by 3 and equation (2) by 4 and add,
$3x+4y=25cosec\theta$
Multiply equation (1) by 4 and equaion (2) by 3 and subtract,
$4x-3y=25\cot \theta$
We know, $cose{c}^2\theta -{\cot }^2\theta =1$
$(3x+4y{)}^2-(4x-3y{)}^{=}{25}^2$
$(3x+4y{)}^2-(4x-3y{)}^{=}625$