Question

find the value of to tan 70=tan20+2tan50

Answer 1

formulae,
1. tan(A+B) = tanA + tanB/1-tanA.tanB
2. tanA = cot(90 - A)
3. tan A.cotA = 1
taking tangent on both sides
tan70 = tan(50 + 20)
using formula (1)
tan70= tan50 + tan20/1-tan50.tan20
tan70.(1-tan50.tan20) = tan50 + tan20
tan70-tan70.tan50.tan20 = tan50 + tan20
tan70 - tan70.tan50.tan(90-70) = tan50 + tan20
tan70-tan70.tan(90-70).tan50 = tan50+tan20
using formulae (2),
tan70-tan70.cot70.tan50 = tan50 + tan20
using formulae (3),
tan70-1.tan50 = tan50 + tan20
tan70 = 2.tan50 = tan 20