Question

Whats the range of 1/(|sinx|) 1/(|cosx| )

Answer 1

let f(x) = 1/|sinx| + 1/|cosx|
we know that AM(Arithmetic mean) is Greater than equal to GM(Geometric mean)use it here .
=> 1/|sinx| + 1/|cosx|______________            >= 1/(|sinx||cosx|)^1/22 so now 
1/|sinx|+1/|cosx| >= 2(2cosec2x)^1/2we know |cosec2x|>= 1
so 
1/sinx +1/cosx >= 2√2
hence range or 
1/|sinx|+|cosx| € [2√2 , ●●)hence range of f(x) is [2√2,●●) .

Answer 2

let the

f(x) = 1/|sinx| + 1/|cosx|

=1/|sinx| + 1/|cosx|

= 1/(|sinx||cosx|)^1/22
1/|sinx|+1/|cosx|

= 2(2cosec2x)^1/22

1/sinx +1/cosx

= 2√2

1/|sinx|+|cosx| ¥ [2√2 , ••)

hence range of f(x) is [2√2,••) .