Question

Cos(a+b)+sinc=sin(a+b)-cosc

Answer 1

To Prove:

Cos(a+ b) + Sin c = Sin(a+ b)-Cos c.

Solution:

For , given angles a, b, and c of a triangle, sum of all angles is 180 degree.

i.e.,

$a+b+c=\pi \\a+b=\pi-c$

therefore,

$cos(a+b)=cos(\pi-c)=-sin (c)\\and \\sin(a+b)=sin(\pi-c)=cos(c)$

Now, to prove,

$L.H.S=cos(a+b)+sin(c)\\=-sin(c)+sin(c)\\=0$      ....(1)

and,

$R.H.S=sin(a+b)-cos(c)\\=cos(c)-cos(c)\\=0$   ...(2)

from equation (1) and (2), L.H.S=R.H.S

Hence, proved.