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Question
State whether the statement is True or False? Also give justification.
If tanθ + tan2θ + `sqrt(3)` tanθ tan2θ = `sqrt(3)`, then θ = `("n"pi)/3 + pi/9`
Options
True
False
Solution
This statement is True.
Explanation:
Given that: tanθ + tan2θ + `sqrt(3)` tanθ tan2θ = `sqrt(3)`
⇒ tanθ + tan2θ = `sqrt(3) - sqrt(3) tan theta tan 2theta`
⇒ tanθ + tan2θ = `sqrt(3) (1 - tan theta tan 2theta)`
⇒ `(tan theta + tan 2theta)/(1 - tan theta tan 2theta) = sqrt(3)`
⇒ tan(θ + 2θ) = `sqrt(3)`
⇒ tan3θ = `tan pi/3`
∴ 3θ = `"n"pi + pi/3`
So θ = `("n"pi)/3 + pi/9`
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