Question

4)
Eliminate thita from the following:
i) x= 6cosec thita , y = 8cot thita
​

Answer 1

Answer:

$\left(\frac{x^{2}}{36}\right)-\left(\frac{y^{2}}{64}\right)=1$

Step-by-step explanation:

$Given \: x = 6cosec\theta$

$\implies cosec\theta=\frac{x}{6}\:--(1)$

$and\\ y = 8cot\theta$

$\implies cot\theta=\frac{y}{8}\:--(2)$

/* We know the , Trigonometric identity:

cosec²A - cot²A = 1 */

$\left(\frac{x}{6}\right)^{2}-\left(\frac{y}{8}\right)^{2}=1$

$\left(\frac{x^{2}}{36}\right)-\left(\frac{y^{2}}{64}\right)=1$

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Answer 2

Step-by-step explanation:

It is given that,

$x=6\csc\theta\ .....(1)\\\\y=8\cot\theta\ ....(2)$

Equation (1) can be rewritten as : $\csc\theta=\dfrac{x}{6}\ .....(3)$

Equation (2) can be rewritten as : $\cot\theta=\dfrac{y}{8}\ .....(4)$

Squaring both equation (3) and (4) and then subtracting :

$\csc^2\theta-\cot^2\theta=(\dfrac{x}{6})^2-(\dfrac{y}{8})^2$

Since, we know that, $\csc^2\theta-\cot^2\theta=1$

So,

$(\dfrac{x}{6})^2-(\dfrac{y}{8})^2=1\\\\\dfrac{x^2}{36}-\dfrac{y^2}{64}=1$

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Trigonometry

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