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Question
If cos A = `4/5`, then the value of tan A is ______.
Options
`3/5`
`3/4`
`4/3`
`5/3`
`1/8`
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Solution
If cos A = `4/5`, then the value of tan A is `underlinebb(3/4)`.
Explanation:
According to the question,
cos A = `4/5` ...(1)
We know,
tan A = `(sin A)/(cos A)`
To find the value of sin A,
We have the equation,
sin2θ + cos2θ = 1
So, sin θ = `sqrt(1 - cos^2θ)`
Then,
sin A = `sqrt(1 - cos^2A)` ...(2)
sin2A = 1 – cos2A
sin A = `sqrt(1 - cos^2A)`
Substituting equation (1) in (2),
We get,
sin A = `sqrt(1 - (4/5)^2)`
= `sqrt(1 - (16/25))`
= `sqrt(9/25)`
= `3/4`
Therefore, tan A = `3/5 xx 5/4 = 3/4`
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