Question

if A B C are angles of a triangle then prove sin (A+B)= sin C​

Answer 1

Good Morning!

Angle A + Alngle B + Angle C = 180

A + B = 180 - C

Taking Sin on both sides we have

Sin ( A + B ) = Sin ( 180 - C )

Sin ( A + B ) = Sin C

Becoz Sin ( 180 - x ) = Sin x

Answer 2

We know that, in a triangle:-

A + B + C = 180°

A + B = 180 - C - - - - - - - - (1)

Now,

Sin ( A + B) = Sin (180 - C) [from eqn 1]

We know that,

Sin (180 - x) = Sin x

Therefore,

Sin(180 - C)= Sin C

So,

Sin (A+B) = Sin C

Hence proved.