If the angle $ heta$ is acute, then the acute angle between $x^{2}\left( \cos heta - \sin heta ight) + 2xy\cos{ heta + y^{2}\left( \cos heta + \sin heta ight) = 0}$ is

Question

If the angle $	heta$ is acute, then the acute angle between $x^{2}\left( \cos	heta - \sin	heta ight) + 2xy\cos{	heta + y^{2}\left( \cos	heta + \sin	heta ight) = 0}$ is

Dr. Abubacker · Accepted Answer

(c)
On comparing the given equation with standard equation, we get
$a = \cos	heta - \sin	heta,\ b = \cos	heta + \sin	heta,\ h = \cos	heta$
$	an\phi = \frac{2\sqrt{\cos^{2}	heta - \left( \cos^{2}	heta - \sin^{2}	heta ight)}}{\cos{	heta - \sin{	heta + \cos{	heta +}\sin	heta}}} = \frac{2\sin	heta}{2\cos	heta}$
$\Rightarrow 	an\phi = 	an	heta \Rightarrow \phi = 	heta$

Q. If the angle $\theta$ is acute, then the acute angle between $x^{2}\left( \cos\theta - \sin\theta \right) + 2xy\cos{\theta + y^{2}\left( \cos\theta + \sin\theta \right) = 0}$ is

Explanation

Reviewed by Dr. Abubacker

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