Question

Prove each of the following identities :
` ((sin A - sin B))/((cos A + cos B)) + (( cos A - cos B))/((sin A + sin B)) =0 `

Answer 1

`LHS=((sinA-sinB)(sinA+sinB)+(cosA-cosB)(cosA+cosB))/((cosA+cosB)(sinA+sin B))`
`=((sin^(2)A-sin^(2)B)+(cos^(2)A-cos^(2)B))/((cosA+cosB)(sinA+sinB))=((sin^(2)A+cos^(2)A)-(sin^(2)B+cos^(2)B))/((cosA+cosB)(sinA+sinB))`
`=((1-1))/((cosA+cosB)(sinA+sinB))=0.`