Question

A, B, and C are 3 angles in triangle ABC then sin(A+B)=?

(a) sinA (b)sinB (c)sinC (d)cosC (e) -sin(A+B)

Answer 1

`sin(A+B)=sinC`

Explanation:

We know that , in `triangleABC`

`A+B+C=pi`

`=>A+B=pi-C`

So,

`sin(A+B)=sin(pi-C)toII^(nd)Quadrant=>sinC >0`

`=>sin(A+B)=sinC`

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Please Carefully, see the image given below to understand the quadrant.

Compare with `color(red)( :pi-theta toII^(nd)Quadrant.`