Tan 20-tan 40-3tan 20-tan 40-

The correct option is A We know that tan(20^∘ + 40^∘) = nbsp; tan 20^∘ + tan 40^∘/1 tan20^∘ tan 40^∘ ⇒ √(3) = nbsp; tan 20^∘ + tan 40^∘/1 tan20^∘ tan ...

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Byju's Answer

Standard XI

Mathematics

Fundamental Laws of Logarithms

tan 20∘+tan 4...

Question

$t a n 20^{\circ} + t a n 40^{\circ} + \sqrt{3} t a n 20^{\circ} t a n 40^{\circ}$ =

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Solution

The correct option is B

We know that $t a n (20^{\circ} + 40^{\circ})$ = $\frac{t a n 20^{\circ} + t a n 40^{\circ}}{1 - t a n 20^{\circ} t a n 40^{\circ}}$

$\Rightarrow$ $\sqrt{3}$ = $\frac{t a n 20^{\circ} + t a n 40^{\circ}}{1 - t a n 20^{\circ} t a n 40^{\circ}}$

$\Rightarrow$ $\sqrt{3}$ - $\sqrt{3}$ $t a n 20^{\circ} t a n 40^{\circ} = t a n 20^{\circ} + t a n 40^{\circ}$

$\Rightarrow$ $t a n 20^{\circ} + t a n 40^{\circ} + \sqrt{3} t a n 20^{\circ} t a n 40^{\circ}$ = $\sqrt{3}$

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tan 20^{\circ} + tan 40^{\circ} + \sqrt{3} tan 20^{\circ} tan 40^{\circ}

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(tan 20^{\circ} + tan 40^{\circ} + \sqrt{3} tan 20^{\circ} tan 40^{\circ})^{2}

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Q. tan 20° + tan 40° +

\sqrt{3}

tan 20° tan 40° is equal to

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\frac{\sqrt{3}}{4}

(b)

\frac{\sqrt{3}}{2}

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(d) 1

Q. Mark the correct alternative in each of the following:

t a n 20^{\circ} + t a n 40^{\circ} + \sqrt{3} t a n 20^{\circ} t a n 40^{\circ}

is equal to

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tan20∘+tan40∘+√3tan20∘tan40∘ =

The correct option is B We know that tan(20∘+40∘) = tan20∘+tan40∘1−tan20∘tan40∘ ⇒ √3 = tan20∘+tan40∘1−tan20∘tan40∘ ⇒ √3 - √3 tan20∘tan40∘=tan20∘+tan40∘ ⇒ tan20∘+tan40∘+√3tan20∘tan40∘ = √3

$t a n 20^{\circ} + t a n 40^{\circ} + \sqrt{3} t a n 20^{\circ} t a n 40^{\circ}$ =