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cos(tan^(-1)(3/4)) =...

`cos(tan^(-1)(3/4)) =`

A

`3/5`

B

`4/5`

C

`4/9`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let `tan^(-1)3/4=x`, where `x in (-pi/2, pi/2)`.
`therefore tanx=3/4` and since `x in (-pi/2, pi/2)`, we have `cosx gt 0`.
`therefore cosx=1/(secx)=1/sqrt(1+tan^(2)x)=1/sqrt(1+9/16)=4/5`.
`therefore cos(tan^(-1)3/4)=cosx=4/5`.
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