Question

If A+B+C =180°, then sin (A+B) - sinC =​

Answer 1

Answer:

A+B+C= 180. A =180-(B+C). join Sin on both sides. => SinA=Sin (B+C).

Answer 2

We have,

sinA +sinB −sinC =2sin(A+B)/2 cos(A−B)/2 − 2sinC/2 cosC/2

Since, (A+B)/2 = 90°−C/2

sin(A+B)/2 = cosC/2

Therefore,

2cosC/2 ⋅ cos(A−B)/2 − 2sinC/2 ⋅ cosC/2

2cosC/2 [cos(A−B) /2−sinC/2]

⇒2cosC/2[cos(A−B)/2 −cos(A+B)/2]

⇒2cosC/2 [2sinA/2 ⋅sinB/2]

⇒4sinA/2 ⋅sinB/2 cosC/2

hope it will help you... have a good day