Question

$If\tan {25}^{\circ }=x,then\frac{\tan {155}^{\circ }-tan{115}^{\circ }}{1+\tan {155}^{\circ }\tan {115}^{\circ }}=\frac{1-x^2}{2x}$.

• A. True
• B. False

Answer 1

The correct option is B False

Given

$\tan {25}^{\circ }=x$

LHS

$\frac{\tan {155}^{\circ }-\tan {115}^{\circ }}{1+\tan {155}^{\circ }\tan {115}^{\circ }}$

$\tan ({155}^{\circ }-{115}^{\circ })$

$\tan {40}^{\circ }$

$\tan ({90}^{\circ }-{50}^{\circ })$

$\cot {50}^{\circ }$

$\frac{1}{\tan {50}^{\circ }}$

$\frac{1}{\tan (2\times 25{)}^{\circ }}$

$\frac{1-{\tan }^2{25}^{\circ }}{2\tan {25}^{\circ }}$

$\frac{1-x^2}{2x}$