Mark the correct alternative in each of the following-tan 20-tan 40-3tan 20-tan 40- is equal to

The correct option is C √(3) tan20^∘ + tan40^∘ + √(3) tan20^∘tan40^∘ = tan60^∘ (1 tan20^∘ tan40^∘)+tan60^∘ tan20^∘ tan40^∘ = tan60^∘ tan60^∘ tan20^∘ tan40^∘ ...

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Byju's Answer

Standard XII

Mathematics

Product of Trigonometric Ratios in Terms of Their Sum

Mark the corr...

Question

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

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

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

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\sqrt{3}

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Solution

The correct option is C $\sqrt{3}$

$t a n 20^{\circ} + t a n 40^{\circ} + \sqrt{3} t a n 20^{\circ} t a n 40^{\circ}$
$= t a n 60^{\circ} (1 - t a n 20^{\circ} t a n 40^{\circ}) + t a n 60^{\circ} t a n 20^{\circ} t a n 40^{\circ}$
$= t a n 60^{\circ} - t a n 60^{\circ} t a n 20^{\circ} t a n 40^{\circ} + t a n 60^{\circ} t a n 20^{\circ} t a n 40^{\circ}$
$= t a n 60^{\circ}$
$= \sqrt{3}$

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Similar questions

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

is equal to

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

Q. tan 20° + tan 40° +

\sqrt{3}

tan 20° tan 40° is equal to

(a)

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

(b)

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

(c)

\sqrt{3}

(d) 1

Q. Solve

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

Q. The numerical value of

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

must be .....

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Mark the correct alternative in each of the following: tan20∘+tan40∘+√3tan20∘tan40∘ is equal to

The correct option is C √3 tan20∘+tan40∘+√3tan20∘tan40∘ =tan60∘(1−tan20∘tan40∘)+tan60∘tan20∘tan40∘ =tan60∘−tan60∘tan20∘tan40∘+tan60∘tan20∘tan40∘ =tan60∘ =√3

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