If cos x= A , cos y = B , sin x= C and sin y = D , find an expression for sin(2x+y) which only involves A , B , C and D .

Answer 1

sin(2x + y) = sin(2x)cosy + cos(2x)siny = 2sinxcosxcosy + (cos²x - sin²x)siny

= 2ABC + (A² - C²)D