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Let f(x)=2 cosec 2x + sec x+cosec x, the...

Let `f(x)=2 cosec 2x + sec x+cosec x`, then the minimum value of `f(x)` for `x in (0,pi/2)` is

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Knowledge Check

  • IF f(x)= sin^2 x + cosec ^2 x , then the minimum value of f(x) is

    A
    1
    B
    `1.5`
    C
    `2`
    D
    3

  • Maximum point of f(x)=cosec x in (-pi,0) is

    A
    `x=-pi//2`
    B
    `x=-pi//3`
    C
    `x=-pi//4`
    D
    none

  • If 0 lt x lt pi/2 and sec x = cosec y , then the value of sin (x + y) is

    A
    0
    B
    1
    C
    `1/2`
    D
    `1/sqrt3`

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    Let f(x)= cosec 2x + cosec^(2)2 x+ cosec^(2)3 x+........+ cosec^(2)n ,x in (0,pi/2) and g(x)=f(x)+cot 2^n x . If H(x)={ [(cosx)^(g(x))+(sec)^(cosecx), if x lt 0], [ p, if x=0] ,[ (e^x+e^(-x)-2cosx)/(x sin x), If x lt 0]} .Find the value of p, if possible to make the function H(x) continuous at x = 0 .

    int (sec x cosec x)/(2 cot x- sec x cosec x)dx=

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