Question

tan theta + cot theta is equal to 2 then, tan squared theta + sin squared theta minus one=?

Answer 1

$\tan \theta + \cot\theta = 2 \\ \tan \theta + \frac{1}{ \tan \theta} = 2 \\ so \: \: \tan \theta = 1 \\ \theta = 45 \: degrees \\ therefore \\ { \tan }^{2} \theta + { \sin }^{2} \theta - 1 \\ = { \tan }^{2} 45 + { \sin }^{2}45 - 1 \\ = {1}^{2} + { (\frac{1}{ \sqrt{2} } )}^{2} - 1 = \frac{1}{2}$