tan 10°+tan 70° - tan 50°

tan A + tan B = cosAcosB sin(A+B) ​ Here we have to prove that tan 1 0∘ + tan ∘ = tan 60 ∘ + tan 50 ∘ ∵ tan 60 ∘ = 3 ​ or cos10 ∘ cos70 ∘ sin60 ∘ ​ = cos60 ∘ cos50 ∘ sin110 ∘ ​ But sin 80 ∘ = cos 10 ∘ , sin 110 ∘ = cos 20 ∘ ∴ sin20 ∘ 1 ​ = cos50 ∘ 2cos20 ∘ ​ ∵cos60 ∘ = 2 1 ​ or cos 50 ∘ = 2 sin 20 ∘ cos 20 ∘ = sin 40 ∘ = cos 50 ∘ by C.R.