Question

express tan in terms of sec

Answer 1

$\huge{ \pink{ \bold{ \boxed{ \star{ \tan( \alpha ) = \frac{ \sin( \alpha ) }{ \cos( \alpha ) } }}}}}$

$\huge{ \pink{ \bold{ \boxed{ \star{ \tan( \alpha ) = \sin( \alpha ) \sec( \alpha ) }}}}}$

Answer 2

$\huge\mathtt{\fcolorbox{red}{gray}{\green{A}\pink{N}\orange{S}\purple{W}\red{E}\blue{R}{!}}}$

Since, we know that

$\mapsto{sec}^{2}A - {tan}^{2}A\:=\:1$

$\mapsto{sec}^{2}A - 1 = {tan}^{2}A$

$\mapsto{tanA\:=\: ± \sqrt{{sec}^{2}A\:-\:1}}$

Hope it helps......

Give me 30 thanks........