Using high school geometry only, show

that sin(A+B) = sinAcosB + sinBcosA

how would i show how one side equals the other side??(Doh)(Shake)(Shake)(Worried)(Surprised)(Wond ering)

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- September 25th 2009, 11:59 AMSneakyproving an addition identity????
Using high school geometry only, show

that sin(A+B) = sinAcosB + sinBcosA

how would i show how one side equals the other side??(Doh)(Shake)(Shake)(Worried)(Surprised)(Wond ering) - September 25th 2009, 01:28 PMKrizalid
consider

http://img243.imageshack.us/img243/9134/recqe9.png

in this figure, we have that NOPR is a rectangle, ON was extended and we get the point M. Join M and P and extend NR, point Q borns. Finally make QP orthogonal to MP and join M and Q.

let and It's easy to prove that

compute and we have it's equal to Multiply the first quotient top and bottom by and in the same fashion for the second quotient by and you'll get the identity.