A) \[\frac{7}{{{a}^{2}}+{{b}^{2}}}\]
B) \[\frac{5}{{{a}^{2}}+{{b}^{2}}}\]
C) \[\frac{7}{{{a}^{2}}-{{b}^{2}}}\]
D) \[\frac{7}{2ab}\]
Correct Answer: D
Solution :
Given, equation are \[a\,\sin \theta +b\,\cos \,\theta =4\] ?.. (i) \[a\,\sin \theta -b\,\,\cos \,\theta =3\] ?? (ii) Adding Eqs. (i), and (ii), we get \[2\,a\,\sin \theta =7\] \[\Rightarrow \] \[\sin \theta =\frac{7}{2a}\] Subtracting Eq. (i) form Eq. (ii) we get \[2b\,\cos \theta =1\] \[\Rightarrow \] \[\cos \theta =\frac{1}{2b}\] Now, \[\sin \,2\theta =2\sin \theta \,\cos \,\theta \] \[=2.\frac{7}{2a}.\frac{1}{2b}\] \[=\frac{7}{2ab}\]
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