A) \[\frac{\pi }{3}\]
B) \[\frac{\pi }{4}\]
C) \[\frac{\pi }{6}\]
D) \[\frac{\pi }{2}\]
E) \[\pi \]
Correct Answer: D
Solution :
The given equation is \[{{x}^{2}}({{\cos }^{2}}\theta -1)-xy{{\sin }^{2}}\theta +{{y}^{2}}{{\sin }^{2}}\theta =0\] On comparing with \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0,\]we get \[a={{\cos }^{2}}\theta -1,h=-\frac{1}{2}{{\sin }^{2}}\theta ,b={{\sin }^{2}}\theta \] \[\because \]\[a+b={{\cos }^{2}}\theta +{{\sin }^{2}}\theta -1=1-1=0\] \[\therefore \]The angle between the pair of straight lines is\[\frac{\pi }{2}\].
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