Question

$\sqrt{3} \tan(a) = 1 \\ find sin {}^{2} a - \: tan {}^{2} a$

Answer 1

$\sqrt{3} \tan( \alpha ) = 1 \\ \tan( \alpha ) = \frac{1}{ \sqrt{3} } \\ \alpha = { \arctan( \frac{1}{ \sqrt{3} } ) } \\ \alpha = 30$
now...

${ (\sin( \alpha ) )}^{2} - ( { \tan( \alpha ) )}^{2} = { (\frac{1}{2}) }^{2} - { (\frac{1}{ \sqrt{3} } )}^{2} \\ \frac{1}{4} - \frac{1}{3}$

-1/12 ans.