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If cos A=4/5, then the value of tanA is...

If `cos A=4/5`, then the value of `tanA` is

A

`3/5`

B

`3/4`

C

`4/3`

D

`5/3`

Text Solution

Verified by Experts

The correct Answer is:
B
Given, cosA=`4/5`
`therefore sinA = sqrt(1-cos^(2)A)` `[therefore sin^(2)A+ cos^(2)A=1]` `[therefore sinA=sqrt(1-cos^(2)A)]`
`=sqrt(1-(4/5)^(2))=sqrt(1-(16/25))=sqrt(9/25)=3/5`
Now, `tanA=(sinA)/(cosA) = (3/5)/(4/5)=3/4`
Hence, the required value of tan A is `3/4`
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