Question

Using the fact that `s in (A + B) = s in A cos B + cos A s in B`and the differentiation, obtain the sum formula for cosines.

Answer 1

`sin(A+B)=sin A cos B +cos A sin B`
Taking A as a function of x and B as constant, differentiate w.r.t. x.
`cos(A+B)*(dA)/(dx)=cosB*cos A(dA)/(dx)+sinB(-sinA)(dA)/(dx)`
`implies cos(A+B)=cosAcosB-sinA sinB`
which is the required formula.