Question

In a $\Delta ABC$, if $\cos A\cos B\cos C=\frac{\sqrt{3}-1}{8}$ and $\sin A.\sin B.\sin C=\frac{3+\sqrt{3}}{8}$, then- On the basis of above information, answer the following questions:The angles of $\Delta ABC$ are:

• A. ${45}^o,{30}^o,{105}^o$
• B. ${45}^o,{60}^o,{75}^o$
• C. ${45}^o,{45}^o,{90}^o$
• D. ${45}^o,{60}^o,{70}^o$

Answer 1

The correct option is B ${45}^o,{60}^o,{75}^o$

$\tan A\tan B\tan C=\frac{\sin A\sin B\sin C}{\cos A\cos B\cos C}=\frac{\frac{3+\sqrt{3}}{8}}{\frac{\sqrt{3}-1}{8}}=\frac{3+\sqrt{3}}{\sqrt{3}-1}=2\sqrt{3}+3=1.\sqrt{3}.(2+\sqrt{3})=\tan 45.\tan 60.\tan 75$

Hence, option 'B' is correct.