The value of tan-tan60- tan60- is

The correct option is C tan 3 θ tan θ tan (60^∘ θ) tan (60^∘+θ) =tan θ×tan 60^∘ tan θ/1 + tan 60^∘ tan θ×tan 60^∘ + tan θ/1 tan 60^∘ tan θ = tan θ×√(3) ...

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Standard X

Mathematics

Standard Values of Trigonometric Ratios

The value of ...

Question

The value of $t a n θ t a n (60^{\circ} - θ) t a n (60^{\circ} + θ)$ is

$c o t 3 θ$

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$2 c o t 3 θ$

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$t a n 3 θ$

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$3 t a n 3 θ$

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Solution

The correct option is C
$t a n 3 θ$

$t a n θ t a n (60^{\circ} - θ) t a n (60^{\circ} + θ) = t a n θ \times \frac{t a n 60^{\circ} - t a n θ}{1 + t a n 60^{\circ} t a n θ} \times \frac{t a n 60^{\circ} + t a n θ}{1 - t a n 60^{\circ} t a n θ} = t a n θ \times \frac{\sqrt{3} - t a n θ}{1 + \sqrt{3} t a n θ} \times \frac{\sqrt{3} + t a n θ}{1 - \sqrt{3} t a n θ} = \frac{t a n θ (3 - t a n^{2} θ)}{1 - 3 t a n^{2} θ} = \frac{3 t a n θ - t a n^{2} θ}{1 - 3 t a n^{2} θ} = t a n 3 θ$

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Similar questions

Q. The value of

\tan θ \tan (60 ° - θ) \tan (60 ° + θ)

is
(a)

\cot 3 θ

(b)

2 \cot 3 θ

(c)

\tan 3 θ

(d)

3 \tan 3 θ

Q. Prove that tan θ tan (60° − θ) tan (60° + θ) = tan 3θ.

Q. General solution of the equation

tan θ tan (60^{\circ} + θ) tan (60^{\circ} - θ) = \sqrt{2} + 1

Prove that:

$t a n θ t a n (60^{\circ} - θ) t a n (60^{\circ} + θ)$

Q. The value of

cosec θ + sec (270 ° - θ) - cosec (270 ° + θ) + sec (180 ° - θ)

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The value of tan θ tan (60∘−θ) tan (60∘+θ) is

The correct option is C tan 3θ tan θ tan (60∘−θ) tan (60∘+θ)=tan θ×tan 60∘−tan θ1+tan 60∘ tan θ×tan 60∘+tan θ1−tan 60∘ tan θ=tan θ×√3−tan θ1+√3 tan θ×√3+tan θ1−√3tan θ=tan θ(3−tan2θ)1−3 tan2θ=3 tan θ−tan2θ1−3 tan2θ=tan 3θ

The value of $t a n θ t a n (60^{\circ} - θ) t a n (60^{\circ} + θ)$ is