isi-entrance 2022 Q8

isi-entrance · India · UGB Trigonometric equations in context
Find the minimum value of $$|\sin x + \cos x + \tan x + \cot x + \sec x + \operatorname{cosec} x|$$ for real numbers $x$ not multiple of $\pi/2$.
Find the minimum value of
$$|\sin x + \cos x + \tan x + \cot x + \sec x + \operatorname{cosec} x|$$
for real numbers $x$ not multiple of $\pi/2$.