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Question
If tanθ = `1/2` and tanΦ = `1/3`, then the value of θ + Φ is ______.
Options
`pi/6`
`pi`
0
`pi/4`
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Solution
If tanθ = `1/2` and tanΦ = `1/3`, then the value of θ + Φ is `bbunderline(pi/4)`.
Explanation:
tanθ = `1/2` and tanΦ = `1/3`
We know that,
tan(θ + Φ) = `(tantheta + tanphi)/(1 - tantheta tanphi)`
= `(1/2 + 1/3)/(1 - 1/2 xx 1/3)`
= `(5/6)/(5/6)`
= 1
⇒ tan(θ + Φ) = `tan pi/4`
⇒ θ + Φ = `pi/4`
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