Question

cos(派/2+a)sin(3派/2-b)+sin(3派/2-a)coa(3派/2-b)=-1/2a属于(派/2,派)b

Answer 1

(-sina)(-cosb)+(-cosa)(-sinb)=-1/2

即sinacosb+cosasinb=-1/2

sin(a+b)=-1/2,

a+b=2kπ-π/6或2kπ-5π/6,k∈Z

又a∈(π/2,π),b∈(π,2π)

则a+b∈(3π/2,3π)

即a+b=2π-π/6

=11π/6