Graph f(x) = sin(3x)/sin(x) - cos(3x)/cos(x) and make a conjecture. Prove your conjecture.

Answer 1

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