If N- tan 20-tan 40-tan 80- 2- then

The correct option is C N is prime ( tan #160;20^∘ #160;tan #160;40^∘ #160;tan #160;80^∘ #160;) ^ 2 we know that tanθtan (60 θ) tan ...

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Standard XII

Mathematics

Real Valued Functions

If N= tan 2...

Question

If $N = {(tan 20^{\circ} tan 40^{\circ} tan 80^{\circ})}^{2}$ , then

N

is prime

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N + 1

is prime

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N^{2}

is prime

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N^{2} + 1

is prime

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Solution

The correct option is C $N$ is prime
${(tan 20^{\circ} tan 40^{\circ} tan 80^{\circ})}^{2}$

we know that $tan θ tan (60 - θ) tan (60 + θ) = tan 3 θ$

$= {(tan 20^{\circ} tan (60^{\circ} - 20^{\circ}) tan (60^{\circ} + 20^{\circ}))}^{2}$

$= {(tan 3 (20^{\circ}))}^{2} = {(tan 60^{\circ})}^{2} = {(\sqrt{3})}^{2} = 3$

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If N=(tan20∘tan40∘tan80∘)2, then

The correct option is C N is prime(tan20∘tan40∘tan80∘)2we know that tanθtan(60−θ)tan(60+θ)=tan3θ=(tan20∘tan(60∘−20∘)tan(60∘+20∘))2=(tan3(20∘))2=(tan60∘)2=(√3)2=3

If $N = {(tan 20^{\circ} tan 40^{\circ} tan 80^{\circ})}^{2}$ , then