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Question
If 5 tan β = 4, then `(5 sin β - 2 cos β)/(5 sin β + 2 cos β)` = ______.
Options
`1/3`
`2/5`
`3/5`
6
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Solution
If 5 tan β = 4, then `(5 sin β - 2 cos β)/(5 sin β + 2 cos β)` = `underline(bb(1/3)`.
Explanation:
Given, 5 tan β = 4
tan β = `4/5`
Now, `(5 sin β - 2 cos β)/(5 sin β + 2 cos β)`
Dividing numerator and denominator by cos β
= `(5 sin β/cos β - 2 cos β/cos β)/(5 sin β/cos β + 2 cos β/cos β)`
= `(5 tan β - 2)/(5 tan β + 2)`
Putting tan θ = `4/5`
= `(5 xx 4/5 - 2)/(5 xx 4/5 + 2)`
= `(4 - 2)/(4 + 2)`
= `2/6`
= `1/3`
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