| If \[7{{\sin }^{2}}\theta +3{{\cos }^{2}}\theta =4,\] then the value of \[tan\theta \]is (\[\theta \] is acute) |
A) \[\frac{1}{\sqrt{2}}\]
B) \[\sqrt{3}\]
C) \[\frac{1}{\sqrt{3}}\]
D) 1
Correct Answer: C
Solution :
| \[7{{\sin }^{2}}\theta +3{{\cos }^{2}}\theta =4\] |
| \[\Rightarrow \]\[7{{\sin }^{2}}\theta +3-3{{\sin }^{2}}\theta =4\]\[\Rightarrow \]\[4{{\sin }^{2}}\theta +3=4\] |
| \[\Rightarrow \] \[{{\sin }^{2}}\theta =\frac{1}{4}\]\[\Rightarrow \]\[\sin \theta =\frac{1}{2}=\sin 30{}^\circ \] |
| \[\Rightarrow \] \[\theta =30{}^\circ \] |
| \[\therefore \] \[tan\theta =tan30{}^\circ =\frac{1}{\sqrt{3}}\] |
You need to login to perform this action.
You will be redirected in
3 sec
