Question

Sin 20
+
Sin 40
=
Sin 80
show that​

Answer 1

To prove

sin 20 + sin 40 = sin 80

LHS :

sin 20 + sin 40 = 2×sin ( (40 +20)/2)× cos ( (40 -20)/2)

{Formula Applied=sin(A)+sin(B)=2*sin(A+B/2)*cos(A-B/2)}

= 2×sin(60/2)×cos(20/2)

= 2×sin(30)×cos(10)

= 2×1/2×cos(10)

= cos 10

= cos ( 90 - 80)

= sin 80 {as cos(90-a)=sin a}

LHS = RHS

Hence Proved