Question

If $\tan 25^{\circ }=x$, then $\frac{\tan 155^{\circ }-\tan 115^{\circ }}{1+\tan 155^{\circ }\tan 115^{\circ }}$ is equal to

• A. $\frac{1-x^2}{2x}$
• B. $\frac{1+x^2}{2x}$
• C. $\frac{1+x^2}{1-x^2}$
• D. $\frac{1-x^2}{1+x^2}$

Answer 1

Answer: (A)

$\frac{\tan \left(180^{\circ }-25^{\circ }\right)-\tan \left(90^{\circ }+25^{\circ }\right)}{1+(\tan \left(180^{\circ }-25^{\circ }\right)\tan \left(90^{\circ }+25^{\circ }\right)}=\frac{-\tan 25^{\circ }+\frac{1}{\tan 25^{\circ }}}{2}=\frac{1-x^2}{2x}$