Trigo Qn

['O' lvl A.Maths standard]

Hi, I need help with this question.

A, B and C are angles in a triangle.

Show that sin A cos B cos C + cos A sin B cos C + cos A cos B sin C = sin A sin B sin C.

starting from the LHS, the most I could get was until

cos A cos B cos C (tan A + tan B + tan C)

Difficult

sin(A+B+C) = 0 as sin 180 degree is 0

Identity:

sin(A+B+C)=sinAcosBcosC+cosAsinBcosC+cosAcosBsinC-sinAsinBsinC

so: sinAcosBcosC + cosAsinBcosC + cosAcosBsinC = sin(A+B+C) + sinAsinBsinC

therefore 0+sinAsinBsinC, proving the eqn

thanks alot!