Question

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

Answer 1

tan(A+B)=tanA+tanB1−tanA.tanB
tanA=cot(90−A)
tanA.cotA=1
We know,70=50+20Taking tangent on both sidestan70=tan(50+20)Using Prerequisite (1)tan70=tan50+tan201−tan50.tan20tan70.(1−tan50.tan20)=tan50+tan20tan70−tan70.tan50.tan20=tan50+tan20tan70−tan70.tan50.tan(90−70)=tan50+tan20tan70−tan70.tan(90−70).tan50=tan50+tan20Using Prerequisite (2)tan70−tan70.cot70.tan50=tan50+tan20Using Prerequisite (3)tan70−1.tan50=tan50+tan20tan70=2.tan50+tan20