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sec(cosec^-1x) is equal to...

`sec(cosec^-1x)` is equal to

A

`cosec(sec^-1x)` for all `x in R`

B

`cosec(sec^-1x)` for `absx gt 1`

C

`absx/sqrt(x^2-1)` for `absx gt 1`

D

cotx

Text Solution

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The correct Answer is:
B, C
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Knowledge Check

  • int cosec x dx is equal to-

    A
    `cosec x cot x+c`
    B
    `log | tan ""(x)/(2)|+c`
    C
    `log | cot ""(x)/(2)|+c`
    D
    `cosec x - cot^(2) x+c`

  • int"cosec"^(4)x dx is equal to -

    A
    `-cot x-(1)/(3) cot^(3) x+c`
    B
    `cot x+(1)/(3)cot^(3)x+c`
    C
    `tan x+(1)/(3) tan^(3)x+c`
    D
    `-cot x+(1)/(3) cot^(3)x+c`

  • int (x^(2)+cos^(2)x)/(x^(2)+1) "cosec"^(2) xdx is equal to -

    A
    `cot x - cot^(-1) x + c`
    B
    ` c - cot x + cot^(-1)x`
    C
    ` - tan^(-1) x - ("cosec x")/(sec x ) + c `
    D
    ` -e ^(log tan^(-1) x - cot x + c `

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