Use the sum-to-product formula to simplify the expression: If sin41∘+sin19∘=sinA∘,0<A<90, then A= ____degrees

Question

please provide all steps for the solution!!!!

Answer 1

The sum-to-product formula states that:

sin(a) + sin(b) = 2[sin((a+b)/2)cos((a-b)/2)].

Therefore,

sin(41°) + sin(19°) = 2[sin((41° + 19°)/2)cos((41° - 19°)/2)]

= 2[sin(30°)cos(11°)]

= 2[(1/2)cos(11°)]

= cos(11°)

Expressing this in terms of its compliment, sine ( sin(a) = cos(90°- a) )

cos(11°) = sin(90° - 11°) = sin(79°)

Therefore, A = 79°.