Question

(iii) sin A sin(A +2B)-sin B sin(B +2 A)
= sin( A - B) sin(A + B)​

Answer 1

Answer:

HELLO DEAR, sin(a + 2b) - sinbsin(b + 2a) ⇒ 2 [ sina sin(a + 2b) - sinbsin(b + 2a) ] /2 ∴ [ multiply and divide by " 2" ]

Answer 2

Answer:

Step-by-step explanation:sina sin(a + 2b) - sinbsin(b + 2a)

⇒ 2 [ sina sin(a + 2b) - sinbsin(b + 2a) ] /2

∴ [ multiply and divide by "2" ]

⇒[ cos(a + 2b - a) - cos(a + 2b + a) - {cos(b + 2a - b) - cos(b + 2a + b) ] /2

∴ [ 2sinAcosB = cos(A - B) - cos(A + B) ]

⇒[ cos(2b) - cos(2a + 2b) - cos(2a) + cos(2a + 2b) ] / 2

⇒[ cos2b - cos2a ] /2

∴ [ cosA - cosB = -2sin(A + B)/2 * sin(A - B)/2 ]

⇒[ -2sin(2a + 2b)/2 * sin(2b - 2a)/2 ] /2

⇒[ -2sin(a + b) * (-)sin(a - b) ] /2

⇒sin(a + b) * sin(a - b)

I HOPE ITS HELP YOU DEAR,

THANKS