Question

what is the value of sec 75 ?

Answer 1

sec75=1.084
thanks........

Answer 2

Given sec 75

$= \ \textgreater \ \frac{1}{cos75}$

$= \ \textgreater \ \frac{1}{sin(90 - 75)}$

$= \ \textgreater \ \frac{1}{sin(15)}$

$= \ \textgreater \ \frac{1}{ \frac{ \sqrt{2 - \sqrt{3} } }{2} }$

$= \ \textgreater \ \frac{2}{ \sqrt{2 - \sqrt{3} } }$

$= \ \textgreater \ \frac{2}{ \sqrt{2- \sqrt{3} } } * \frac{ \sqrt{2 - \sqrt{3} } }{ \sqrt{2 - \sqrt{3} } }$

$= \ \textgreater \ \frac{2 \sqrt{2 - \sqrt{3} } }{2 - \sqrt{3} }$

$= \ \textgreater \ \frac{2 \sqrt{2 - \sqrt{3} } }{2 - \sqrt{3} } * \frac{2 + \sqrt{3} }{2 + \sqrt{3} }$

$= \ \textgreater \ \frac{2(2 + \sqrt{3}) \sqrt{2 - \sqrt{3} } }{(2)^2 - ( \sqrt{3})^2 }$

$= \ \textgreater \ \frac{2(2 + \sqrt{3}) \sqrt{2 - \sqrt{3} } }{1}$

$= \ \textgreater \ 2(2 + \sqrt{3} ) (\sqrt{2- \sqrt{3} } )$



Hope this helps!