if A+B+C=180 then show that sin(B+C)sinA
Answers (3)
17th Apr, 2020
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
Comments (0)
30th Nov, 2019
Now you have made some typing mistake there.
But the question should have been
A+B+C=180
Then show that
sin(B+C)=sin(A)
Now A+B+C=180
or,B+C=180-A
sin(B+C)=sin(180-A)
=sin(2*90-A)....(1)
So The sin wouldn't change to cos as 180=2*90
i.e even multiple of 90.
and the angle is in 2nd quadrant.
sin is positive in 2nd quadrant.
So from equation 1
sin(B+C)=sinA
But the question should have been
A+B+C=180
Then show that
sin(B+C)=sin(A)
Now A+B+C=180
or,B+C=180-A
sin(B+C)=sin(180-A)
=sin(2*90-A)....(1)
So The sin wouldn't change to cos as 180=2*90
i.e even multiple of 90.
and the angle is in 2nd quadrant.
sin is positive in 2nd quadrant.
So from equation 1
sin(B+C)=sinA
Comments (0)
30th Nov, 2019
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
Comments (0)
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