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if A+B+C=180 then show that sin(B+C)sinA


Suraj 30th Nov, 2019
Answers (3)
lubhan cherwoo 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

Avishek Dutta 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
Malini S N 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

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