Question

If $A$ and $B$ are measures of an acute angles, $\tan A=\frac{1}{\sqrt{3}}$ and $\sin B=\frac{1}{2}$ then $\cos (A+B)=$

• A. $0$
• B. $\frac{\sqrt{3}}{2}$
• C. $\frac{1}{2}$
• D. $\frac{1}{\sqrt{3}}$

Answer 1

Answer: (C)

$\frac{1}{2}$

$\tan A=\frac{1}{\sqrt{3}}$

$\sin B=\frac{1}{2}$

$\cos (A+B)=?$

$\frac{\sin A}{\cos \left(A\right)}=\frac{1}{2}\times \frac{2}{\sqrt{3}}$

$\sin A=\frac{1}{2}\sin B=\frac{1}{2}\Rightarrow B={30}^0$

$\cos A=\frac{\sqrt{3}}{2}=A={30}^0$

$\cos (A+B)=\cos ({30}^0+{30}^0)$

$=\cos {60}^0=\frac{1}{2}$Ans.