Question : What is the value of $\left( an 10^{\circ} an 80^{\circ}+ an 20^{\circ} an 70^{\circ}+ an 30^{\circ} an 60^{\circ}+ an 40^{\circ} an 50^{\circ} ight)$?
Option 1: 4
Option 2: 3
Option 3: 5
Option 4: 2

Question

Question : What is the value of $\left( an 10^{\circ} an 80^{\circ}+ an 20^{\circ} an 70^{\circ}+ an 30^{\circ} an 60^{\circ}+ an 40^{\circ} an 50^{\circ} ight)$?

Option 1: 4

Option 2: 3

Option 3: 5

Option 4: 2

Team Careers360 · Accepted Answer

Correct Answer: 4

Solution : Given: $( an 10^{\circ} an 80^{\circ}+ an 20^{\circ} an 70^{\circ}+ an 30^{\circ} an 60^{\circ}+ an 40^{\circ} an 50^{\circ})$
$= an 10^{\circ} an (90^{\circ}-10^{\circ})+ an 20^{\circ} an (90^{\circ}-20^{\circ})+ an 30^{\circ} an (90^{\circ}-30^{\circ})+ an 40^{\circ} an (90^{\circ}-40^{\circ})$
$= an 10^{\circ} \cot 10^{\circ}+ an 20^{\circ} \cot 20^{\circ}+ an 30^{\circ} \cot 30^{\circ}+ an 40^{\circ} \cot 40^{\circ}$
$=1+1+1+1$
$=4$
Hence, the correct answer is 4.

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Question : What is the value of (tan⁡10∘tan⁡80∘+tan⁡20∘tan⁡70∘+tan⁡30∘tan⁡60∘+tan⁡40∘tan⁡50∘)?Option 1: 4Option 2: 3Option 3: 5Option 4: 2

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Question : What is the value of $(\tan 10^{\circ} \tan 80^{\circ} + \tan 20^{\circ} \tan 70^{\circ} + \tan 30^{\circ} \tan 60^{\circ} + \tan 40^{\circ} \tan 50^{\circ})$ ?
Option 1: 4
Option 2: 3
Option 3: 5
Option 4: 2