Question

In triangle ABC prove that
(i) `sinA=sin(B+C)" "(ii) sin2A=-sin(2B+2C)`
(iii)` cosA=-cos(A+B)" " (iv) tan((A+B)/2)=cot. C/2`

Answer 1

`(i) sinA=sin(pi-(B+C))=sin(B+C)`
`(ii) sin2A=sin(2pi-(2B+2C))=-sin(2B+2C)`
`(iii)cosA=cos(pi-(B+C))=-cos(B+C)`
`(iv) tan((A+B)/2)=tan((pi-C)/2)=tan(pi/2-C/2)=cot(C/2)`