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If sec x + tan x =22/7 , find the value ...

If sec x + tan x =22/7 , find the value of tanx/2

A

the value of tan `(x)/(2)=(29)/(15)`

B

the value of tan `(x)/(2)=(29)/(15)`

C

the value of cosec x + cot `x=(29)/(15)`

D

thevalue of cosec x + cot `x=(15)/(29)`

Text Solution

Verified by Experts

The correct Answer is:
B, C

`sec x + tan x = (22)/(7)`
`rArr (1+sin x)/(cos x)=(22)/(7)`
`rArr (1+(2t)/(1+t^(2)))/((1-t^(2))/(1+t^(2)))=(22)/(7)`, where `t= tan.(x)/(2)`
`rArr ((1+t)^(2))/(1-t^(2))=(22)/(7)`
`rArr (1+t)/(1-t)=(22)/(7)`
`rArr t=(15)/(29)`
Now cosec x + cot x
`=(1+cos x)/(sin x)`
`=(2 cos^(2)(x//2))/(2sin(x//2)cos(x//2))`
`=cot((x)/(2))=(29)/(15)`
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Knowledge Check

  • If cot^(-1) x = (2pi)/7 for some x in R the value of tan^(-1) x is :

    A
    `(3pi)/14`
    B
    `(-3pi)/14`
    C
    `(7pi)/12`
    D
    `(-7pi)/2`
  • If sec theta = x + (1)/(4x) , then sec theta + tan theta =

    A
    x,`(1)/(x)`
    B
    `2x, (1)/(2x)`
    C
    `-2x, (1)/(2x)`
    D
    `-x,(1)/(x)`,x
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