A) 0
B) 1
C) \[\frac{1}{4}\]
D) \[\frac{1}{2}\]
Correct Answer: A
Solution :
\[\frac{5\cos \theta -4}{3-5\sin \theta }-\frac{3+5\sin \theta }{4+5\cos \theta }\] \[=\frac{(5\cos \theta -4)(4+5\cos \theta )-(3+5\sin \theta )(3-5\sin \theta )}{(3-5\sin \theta )(4+5\cos \theta )}\]\[=\frac{(25{{\cos }^{2}}\theta -16)-(9-25{{\sin }^{2}}\theta )}{(3-5\sin \theta )(4+5\cos \theta )}\] \[=\frac{25({{\sin }^{2}}\theta +{{\cos }^{2}}\theta )-25}{(3-5\sin \theta )(4+5\cos \theta )}=\frac{25-25}{(3-5\sin \theta )(4+5\cos \theta )}=0\]
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