Prove that : tan 70° = 2tan 50° + tan 20°.

Formula: - (i)

(ii) tan(90° – A) = cot A

Taking formula (i)

⇒ tanA – tanB = tan(A – B)(1 + tanAtanB)

⇒ tan70° – tan20° = tan(70° – 20°)(1 + tan70°tan20°)

⇒ tan70° – tan20° = tan50°(1 + tan70°cot70°) - - - - from formula (ii)

⇒ tan70° – tan20° = 2tan50°

L.H.S = R.H.S