Question

Solve for x: sin(x+pi/4)-sin(x-pi/4)=1
I have used the sum and difference formulas and got: (sin(x)cos(pi/4)+cos(x)sin(pi/4))-(sin(x)cos(pi/4)-cos(x)sin(pi/4)) I'm not sure where to go from there. I think I can use the double angle identity, but I'm not sure how.

Answer 1

first can you expand this?
\[(\sin(x)\cos(\pi/4)+\cos(x)\sin(\pi/4))-(\sin(x)\cos(\pi/4)-\cos(x)\sin(\pi/4))\]

Answer 2

\[(\color{red}{\sin(x)\cos(\pi/4)}+\cos(x)\sin(\pi/4))-(\color{red}{\sin(x)\cos(\pi/4)}-\cos(x)\sin(\pi/4))\]

look at the terms marked in red... what happens to them?

Answer 3

Would they cancel out?