Question

$\frac{\sin {70}^o+\cos {40}^o}{\cos {70}^o+\sin {40}^o}=$

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

Answer 1

The correct option is B $\sqrt{3}$

$\frac{\sin {70}^o+\cos {40}^o}{\cos {70}^o+\sin {40}^o}=\frac{\sin {70}^o+\sin {50}^o}{\cos {70}^o+\cos {50}^o}$

$=\frac{2\sin {60}^o\cos {10}^o}{2\cos {60}^o\cos {10}^0}=\tan {60}^0=\sqrt{3}$