Question

Question 19 Prove that [sin(x) + sin(3x)] / [cos(x) + cos(3x)] = tan(2x)

Class X1 - Maths -Trigonometric Functions Page 73

Answer 1

LHS = (sinx + sin3x)/(cosx + cos3x)
use the formula,
sinC + sinD = 2sin(C+D)/2.cos(C-D)/2
cosC + cosD = 2cos(C+D)/2.cos(C-D)/2

= {2sin(x + 3x)/2.cos(3x -x)/2}/{2cos(x + 3x)/2.cos(3x -x)/2}
= {sin2x.cosx}/{cos2x.cosx}
=tan2x = RHS