Question

Find the value of tan83° tan38° + tan83 - tan38°.​

Answer 1

Answer:

√3

tan7 ∘ tan23°tan60∘tan67∘tan83∘

tan60∘tan67∘tan83∘We know that,

tan60∘tan67∘tan83∘We know that,cotθ=tanθ1

tan60∘tan67∘tan83∘We know that,cotθ=tanθ1tan(90− θ)= cotθ

tan60∘tan67∘tan83∘We know that,cotθ=tanθ1tan(90− θ)= cotθtan7∘= tan(90∘− 83∘)= cot83∘

tan60∘tan67∘tan83∘We know that,cotθ=tanθ1tan(90− θ)= cotθtan7∘= tan(90∘− 83∘)= cot83∘tan23∘= tan(90∘

= tan(90∘− 67

= tan(90∘− 67∘

= tan(90∘− 67∘)= cot67

= tan(90∘− 67∘)= cot67∘

= tan(90∘− 67∘)= cot67∘∴ tan7

= tan(90∘− 67∘)= cot67∘∴ tan7∘

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘tan83

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘tan83∘

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘tan83∘=

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘tan83∘= tan83

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘tan83∘= tan83∘

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘tan83∘= tan83∘1

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘tan83∘= tan83∘1tan67

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘tan83∘= tan83∘1tan67∘

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘tan83∘= tan83∘1tan67∘1

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘tan83∘= tan83∘1tan67∘1tan60

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘tan83∘= tan83∘1tan67∘1tan60∘

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘tan83∘= tan83∘1tan67∘1tan60∘tan67

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘tan83∘= tan83∘1tan67∘1tan60∘tan67∘

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘tan83∘= tan83∘1tan67∘1tan60∘tan67∘tan83

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘tan83∘= tan83∘1tan67∘1tan60∘tan67∘tan83∘

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘tan83∘= tan83∘1tan67∘1tan60∘tan67∘tan83∘=

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘tan83∘= tan83∘1tan67∘1tan60∘tan67∘tan83∘= tan83

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘tan83∘= tan83∘1tan67∘1tan60∘tan67∘tan83∘= tan83∘

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘tan83∘= tan83∘1tan67∘1tan60∘tan67∘tan83∘= tan83∘tan67

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘tan83∘= tan83∘1tan67∘1tan60∘tan67∘tan83∘= tan83∘tan67∘

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘tan83∘= tan83∘1tan67∘1tan60∘tan67∘tan83∘= tan83∘tan67∘tan60

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘tan83∘= tan83∘1tan67∘1tan60∘tan67∘tan83∘= tan83∘tan67∘tan60∘

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘tan83∘= tan83∘1tan67∘1tan60∘tan67∘tan83∘= tan83∘tan67∘tan60∘tan67

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘tan83∘= tan83∘1tan67∘1tan60∘tan67∘tan83∘= tan83∘tan67∘tan60∘tan67∘

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘tan83∘= tan83∘1tan67∘1tan60∘tan67∘tan83∘= tan83∘tan67∘tan60∘tan67∘tan83∘= tan60∘

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘tan83∘= tan83∘1tan67∘1tan60∘tan67∘tan83∘= tan83∘tan67∘tan60∘tan67∘tan83∘= tan60∘=

= tan(90∘− 67∘)= cot67∘∴ tan7∘tan23∘tan60∘tan67∘tan83∘=cot83∘cot67∘tan60∘tan67∘tan83∘= tan83∘1tan67∘1tan60∘tan67∘tan83∘= tan83∘tan67∘tan60∘tan67∘tan83∘= tan60∘=3