Hi,
A+B+C= 180.
A =180-(B+C).
join Sin on both sides.
=> SinA=Sin (180-(B+C)
=> SinA=Sin (B+C).
Given that,
=> SinA+Sin (B-C)
=> Sin (B+C)+Sin (B-C).
We know the formula,
Sin (B+C) = SinB.CosC+CosB. SinC
Sin (B-C) = SinB. CosC -CosB. SinC.
By adding we get,
=> SinB.CosC +CosB. SinC +SinB. CosC -CosB. SinC.
=> 2SinB.CosC.
So,
=> SinA +Sin (B-C) = 2SinB.CosC.
Read more on Brainly.in - https://brainly.in/question/3684628#readmore
A+B+C=180
B+C=180-A
sin(B+C)=sin(180-A)=sinA (As,sin(180- θ)=sin θ)
So,sin(B+C) = sinA
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