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The value of cot[cos^(-1)(7/25)] is...

The value of `cot[cos^(-1)(7/25)]` is

A

`25/24`

B

`25/7`

C

`24/25`

D

`7/24`

Text Solution

Verified by Experts

The correct Answer is:
D
We have, `cot[cos^(-1)(7/25)]`
Let `cos^(-1)'(7)/(25) = x`
`rArr cosx = 7/25`
`:. sin x = sqrt(1-cos^(2)x) = sqrt(1-(7/25)^(2))`
`= sqrt((625-49)/(625)) = 24/25`

`:. cot x = (cosx)/(sinx) = (7/25)/(24/25) = 7/24`
`rArr x = cot^(-1)(7/24) = cos^(-1)(7/25)`
`:. cot(cos^(-1)'7/25) = cot(cot^(-1)'7/24) = 7/24 , [:' cot^(-1)'7/24 = cos^(-1)'(7)/(25)]`
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