Question

if x is equal 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:

The question should have been sec theta instead of sin theta

Step-by-step explanation:

This is the equation of a hyperbola

The proof is attached in the image below

Answer 2

LHS = RHS

Step-by-step explanation:

given :

$x = a\sin \theta , Y = b\tan\theta$

then we have to prove

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

taking LHS

$\frac{a^2}{x^2}-\frac{b^2}{y^2}\\\\\frac{a^2}{(a\sin \theta)^2}-\frac{b^2}{(b\tan\theta)^2}\\\\\frac{1}{\sin^2\theta}- \frac{1}{\tan^2\theta }$

we know that $\tan^2\theta = \frac{\sin^2\theta}{\cos^2\theta}$

therefore ,

$\frac{1}{\sin^2\theta}- \frac{1}{\tan^2\theta }\\\\\frac{1}{\sin^2\theta}- \frac{\cos^2\theta}{\sin^2\theta }\\\\\frac{1-\cos^2\theta}{\sin^2\theta}\\\\\ast \sin^2\theta +\cos^2\theta=1 \\\\1-\cos^2\theta= \sin^2\theta\\\\therefore , \\\\\frac{1-\cos^2\theta}{\sin^2\theta} = \frac{\sin^2\theta}{\sin^2\theta}=1 = RHS$

hence proved

#Learn more :

https://brainly.in/question/12537419