Question

Prove tan70 = 2tan50 + tan20

Answer 1

tan70° = tan( 50° + 20°)
tan70° = tan50° + tan20°/ 1 - tan50°tan20° 
.......Using tan (A +B) = tanA +tanB/1 - tanAtanB
=>tan70°(1 - tan50°tan20°) = tan50° + tan20°
=>tan70° - tan50°tan20°tan70° = tan50° + tan20°
=>tan70° - tan50° = tan50° + tan20° ..........( tan20° x tan70° = 1)
=>tan70° = tan50° + tan50° + tan20°
=>tan70° = 2tan50° + tan20°

Answer 2

⇒tan 70 = tan(50+20)
⇒tan 70= (tan 50 + tan20)/(1-tan50* tan20)
⇒tan 70- tan 70*tan50*tan20 = tan 50 +tan20
⇒tan 70- tan 50 =tan50+tan20 
⇒tan 70 = 2tan50 +tan20