A) \[\sqrt{3}\]
B) \[1\]
C) \[0\]
D) \[\frac{1}{\sqrt{3}}\]
Correct Answer: D
Solution :
| [d]\[7{{\sin }^{2}}A+3{{\cos }^{2}}A=4\] |
| \[\Rightarrow \,\,\,4{{\sin }^{2}}A+3({{\sin }^{2}}A+{{\cos }^{2}}A)=4\] |
| \[\Rightarrow \,\,\,\,\,4{{\sin }^{2}}A+3\times 1=4\]\[[{{\sin }^{2}}\theta +{{\cos }^{2}}\theta =1]\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,4{{\sin }^{2}}A=1\,\,\,\,\,\,\,\,\Rightarrow \,\,\,\,\,\sin A=\frac{1}{2}=\sin 30{}^\circ \] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,A=30{}^\circ \] |
| \[\therefore \,\,\,\,\,\,\,\,\,\,\,\tan A=\tan 30{}^\circ =\frac{1}{\sqrt{3}}\] |
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