If tan-tan-3-tan-3-a tan 3 - then a is equal to

The correct option is D 3We have, tanθ+tan(π/3+θ )+tan( π/3+θ )=a tan 3θ ⇒ tanθ+√(3)+tanθ/1 √(3)tanθ+tanθ √(3)/1+√(3)θ=a tan 3θ ⇒ tanθ+8tanθ/1 3tanθ=a tan 3θ ⇒ ...

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Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios for Sum of Two Angles

If tanθ+tanπ/...

Question

If $t a n θ + t a n (\frac{π}{3} + θ) + t a n (- \frac{π}{3} + θ) = a t a n 3 θ$ , then a is equal to

1/3

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None of these

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Solution

The correct option is C 3
We have,
$t a n θ + t a n (\frac{π}{3} + θ) + t a n (- \frac{π}{3} + θ) = a t a n 3 θ$
$\Rightarrow t a n θ + \frac{\sqrt{3} + t a n θ}{1 - \sqrt{3} t a n θ} + \frac{t a n θ - \sqrt{3}}{1 + \sqrt{3} θ} = a t a n 3 θ$
$\Rightarrow t a n θ + \frac{8 t a n θ}{1 - 3 t a n θ} = a t a n 3 θ$
$\Rightarrow \frac{3 (3 t a n θ - t a n^{3} θ)}{(1 - 3 t a n^{2} θ)} = a t a n 3 θ$
$\Rightarrow 3 t a n 3 θ = a t a n 3 θ$
$\Rightarrow a = 3$

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If tanθ+tan(π3+θ)+tan(−π3+θ)=a tan 3θ, then a is equal to

The correct option is C 3We have, tanθ+tan(π3+θ)+tan(−π3+θ)=a tan 3θ ⇒tanθ+√3+tanθ1−√3tanθ+tanθ−√31+√3θ=a tan 3θ ⇒tanθ+8tanθ1−3tanθ=a tan 3θ ⇒3(3 tanθ−tan3θ)(1−3tan2θ)=a tan 3θ ⇒3 tan 3θ=atan 3θ ⇒a=3

If $t a n θ + t a n (\frac{π}{3} + θ) + t a n (- \frac{π}{3} + θ) = a t a n 3 θ$ , then a is equal to