ЯсноПонятно24

To simplify the given expression, we will expand the product of the two binomials:

(sinx + cosx)(√3siny + cosy) = sinx√3siny + sinxcosy + cosx√3siny + cosxcosy = sinx√3siny + cosx√3siny + sinxcosy + cosxcosy = √3sinxcosy + sinxcosy + cosxcosy

Now, we can factor out a sinxcosy from the expression:

= sinxcosy(√3 + 1) + cosxcosy

Since sinxcosy = sin(2x)/2, we can substitute this back into the expression:

= sin(2x)/2(√3 + 1) + cosxcosy

Now, we can simplify further:

= sin(2x)(√3 + 1)/2 + cosxcosy

Therefore, the simplified expression is sin(2x)(√3 + 1)/2 + cosxcosy.