Posted by Natalie on .
Graph f(x) = sin(3x)/sin(x)  cos(3x)/cos(x) and make a conjecture. Prove your conjecture.

Precalculus with Trigonometry 
Reiny,
http://www.wolframalpha.com/input/?i=plot+sin%283x%29%2Fsin%28x%29++cos%283x%29%2Fcos%28x%29+
mmmhhhh?
let y = sin(3x)/sin(x)  cos(3x)/cos(x)
= (sin(3x)cos(x)  cos(3x)sinx)/(sinxcosx)
= sin(3x  x)/(sinxcos)
= sin(2x)/sinxcosx
= 2sinxcosx/(sinxcosx)
= 2
so it is a straight line y = 2 as shown in the graph