Question

Question 18 Prove that [sin(x) - sin(y)] / [cos(x) + cos(y)] = tan [ (x-y) / 2 ]

Class X1 - Maths -Trigonometric Functions Page 73

Answer 1

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

= {2cos(x+y)/2.sin(x-y)/2}/{2cos(x +y)/2.cos(x -y)/2}
= {sin(x - y)/2}/{cos(x-y)/2}
= tan(x - y)/2 = RHS