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If tan theta = 1/(sqrt(11)) and 0 < thet...

If `tan theta = 1/(sqrt(11)) and 0 < theta < pi/2`, then the value of `("cosec^2 theta - sec^2 theta)/(cosec^2 theta + sec^2 theta)` is

A

`3/4`

B

`4/5`

C

`5/6`

D

`6/7`

Text Solution

Verified by Experts

The correct Answer is:
C
`tan theta = 1/sqrt(11) implies tan theta = 1/(11)`
`(cosec^2 theta - sec^2 theta)/(cosec^2 theta + sec^2 theta)= (cos^2 theta - sin^2 theta)/(cos^2 theta + sin^2 theta)`
`= (1-tan^2 theta)/(1+ tan^2 theta) = (1- 1/(11))/(1+ 1/(11)) = (10)/(12)`
= `5/6`
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Knowledge Check

  • If sec theta - 1 = (sqrt2 -1) tan theta , then theta =

    A
    `2npi`
    B
    `2 npi + pi/4`
    C
    `2 n pi- pi/4`
    D
    `2n pi + pi/3`

  • If : tan theta - sqrt(2) cdot "sec" theta = sqrt(3) , then : theta =

    A
    `npi +(-1)^(n) cdot pi/4 - pi/3`
    B
    `npi +(-1)^(n) cdot pi/3 - pi/4`
    C
    `npi +(-1)^(n) cdot pi/3 + pi/4`
    D
    `npi +(-1)^(n) cdot pi/4 + pi/3`

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