['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!