Question

Find the value of sin 50 + sin 70 - sin 10

Answer 1

sin 50 - sin 70= 2 cos ((50+70)/2) sin ((50-70)/2)
                          = 2 cos (120/2) sin(-20/2) 
                          = 2 cos 60 sin (-10)
sin 50 - sin 70= -sin 10       [cos 60= 1/2 and  sin(-A)= -sin A]
Therefore, sin 50 - sin 70 + sin 10= -sin 10 + sin 10= 0