Question

The value of $\frac{\sin {70}^o+\cos {40}^o}{\cos {70}^o+\sin {40}^o}$, is

• A. $2\sqrt{3}$
• B. $4\sqrt{3}$
• C. $\sqrt{3}$
• D. $Noneofthese$

Answer 1

Answer: (C)

$\sqrt{3}$

$\frac{sin{70}^0+cos{40}^0}{cos{70}^0+sin{40}^0}=\frac{Cos{20}^0+Cos{40}^0}{Sin{20}^0+sin{40}^0}=\frac{2cos{30}^{0}Cos{10}^0}{2sin{30}^{0}cos{10}^0}=cot{30}^0=\sqrt{3}$