Question

if f(x)=cos²+sec²
then f(x)=
a]≤1
b]≥1
c]≤2
d]≥2

kindly answer with full explaination

Answer 1

$solution \\ here \: we \: can \: use \: relation \: betweem \\ \: arthematic \: mean \: and \: geometric \: mean \\ am \geqslant gm \\ so \: \\ \frac{{ ( \cos( x ) ) }^{2} + { (\sec( x )) }^{2} }{2} \geqslant \sqrt{ { (\cos( x )) }^{2} { (\sec( x ) )}^{2} } \\ \frac{f(x)}{2} \geqslant \cos(x ) \sec(x) \\ f(x) \geqslant (2)1 \\ therefore \: the \: answer \: is \: \\ \geqslant 2 \\ hope \: it \: helps$