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Tan 7° tan23° tan60° tan67° tan83°= …

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Tan 7° tan23° tan60° tan67° tan83°= √3
  • 2 answers

Faisal Khan 2 months ago

Solution verified Verified by Toppr To evaluate, tan7 ∘ tan23 ∘ tan60 ∘ tan67 ∘ tan83 ∘ We know that, tan(90−θ)=cotθ and cotθ= tanθ 1 ​ tan7 ∘ =tan(90 ∘ −83 ∘ )=cot83 ∘ tan23 ∘ =tan(90 ∘ −67 ∘ )=cot67 ∘ ∴tan7 ∘ tan23 ∘ tan60 ∘ tan67 ∘ tan83 ∘ =cot83 ∘ cot67 ∘ tan60 ∘ tan67 ∘ tan83 ∘ = tan83 ∘ 1 ​ tan67 ∘ 1 ​ tan60 ∘ tan67 ∘ tan83 ∘ = tan83 ∘ tan67 ∘ tan60 ∘ tan67 ∘ tan83 ∘ ​ =tan60 ∘ = 3 ​ Solve any question of Introduction to Trigonometry with:-

Shreya Khamithkar 2 months, 1 week ago

Tan(90-theta)=cot theta Change tan 83, tan(90-83)=cot 7 Then also change tan 23, tan(90-23)=cot 67, We know tan 60=√3, Put the values Tan7.cot67.tan60.tan67.cot7 =√3 We know tan theta x cot theta =1 Tan7.cot7.tan67.cot67.√3=√3 1.1.√3=√3 √3=√3 LHS=RHS *(.) Symbolises mulplication here I hope you understood my answer Thank u
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