Question

9. Show that sec2 x + cosec2 x > 4.​

Answer 1

Step-by-step explanation:

sec²x+ cosec²x

=>1+tan²x+ 1+cot²x

=>tan²x+1/tan²x+2

=>(tan x+1/tan x)².......equ(i)

we know from AM-GM inequality,

a+1/a≥2 (when a>0)

so,

(a+1/a)²≥4.....equ(ii)

on comparing equ(i) and equ(i),,

we conclude that,

sec²x+cosec²x≥4