Question

$\frac{\cos {25}^o+\sin {25}^o}{\cos {25}^o-\sin {25}^o}$=

• A. $\tan {70}^o$
• B. $\tan {56}^o$
• C. $\tan {54}^o$
• D. $\tan {73}^o$

Answer 1

The correct option is A $\tan {70}^o$

$\frac{\cos {25}^{\circ }+\sin {25}^{\circ }}{\cos {25}^{\circ }-\sin {25}^{\circ }}$

$=\frac{1+\tan {25}^{\circ }}{1-\tan {25}^{\circ }}$

$=\frac{{45}^{\circ }+\tan {25}^{\circ }}{1-(\tan {45}^{\circ }\times \tan {25}^{\circ })}$

$=\tan (25+45{)}^{\circ }=\tan {70}^{\circ }$