Question

if x is equals to a sin theta and Y is equal to B tan theta then prove that a square by x square minus b square by y square is equals to 1​

Answer 1

Answer:

proved

Step-by-step explanation:

theta = ∝

x = asin∝  , y = btan∝

a²/x² - b²/y² = 1/sin²∝ - 1/tan²∝ = cosec²∝ - cot²∝ = 1

Answer 2

$\bold{\dfrac{a^2}{x^2}-\dfrac{b^2}{y^2} = 1}$

Step-by-step explanation:

We are given the following int the question:

$x = a \sin \theta\\y = b \tan \theta$

We have to evaluate:

$\dfrac{a^2}{x^2}-\dfrac{b^2}{y^2}$

Putting, the values, we get:

$\dfrac{a^2}{x^2}-\dfrac{b^2}{y^2}\\\\=\dfrac{a^2}{a^2\sin^2 \theta}- \dfrac{b^2}{b^2\tan^2 \theta}\\\\=\dfrac{1}{\sin^2 \theta}- \dfrac{1}{\tan^2 \theta}\\\\= \textrm{cosec}^2 \theta - \cot^2 \theta\\\text{By the trignometric identity}\\= 1$

#Learnmore

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