A) \[7:1\]
B) \[5:3\]
C) \[9:7\]
D) \[3:1\]
Correct Answer: A
Solution :
\[a=\sqrt{3}+1\] |
\[b=\sqrt{3}-1\] |
\[\frac{\sin A}{\sin B}=\frac{\sqrt{3}+1}{\sqrt{3}-1}\] |
\[=\frac{3+1+2\sqrt{3}}{2}=2+\sqrt{3}\] |
\[\frac{\sin A}{\sin (120-A)}=\sqrt{3}+2\] |
\[\frac{\sin A}{\sin 12\operatorname{cosA}-cos12sinA}=\sqrt{3}+2\] |
\[\frac{1}{\frac{\sqrt{3}}{2}\cot A+\frac{1}{2}}=\sqrt{3}+2.\] |
\[\frac{\sqrt{3}\cot A+1}{2}=\frac{1}{\sqrt{3}+2}=\frac{\sqrt{3}-1}{-1}\] |
\[\frac{\sqrt{3}\cot A+1}{2}=-\sqrt{3}+2\] |
\[\sqrt{3}\cot A=4-2\sqrt{3}-1\] |
\[\sqrt{3}\cot A=3-2\sqrt{3}\] |
\[\cot A=\sqrt{3}-2\] |
\[-\cot A=2-\sqrt{3}=\tan 15\] |
\[\therefore \] \[A=105{}^\circ \] |
\[\therefore \] \[B=15{}^\circ .\] |
You need to login to perform this action.
You will be redirected in
3 sec