## anonymous one year ago sin (x+(pi/4))-sin (x-(pi/4))=1 Help to solve for solutions?

1. anonymous

one way would be to rewrite the left hand side as a single trig function it will take a raft of steps, but i think you get $\sqrt{2}\cos(x)$

2. anonymous

then it should be very easy you need to use the addition angle formula, and the subtraction angle formula for sine

3. anonymous

Sin (x+π/4)=sin x cos (π/4)+cos x sin (π/4) sin (x-π/4)=sin x cos (–π/4)-cos x sin( –π/4) Would using the sum/difference formulas help to solve? The question says they should be used but I'm not sure where to go from here.

4. anonymous

some of those are numbers right?

5. anonymous

$\frac{\sqrt{2}}{2}\sin(x)+\frac{\sqrt{2}}{2}\cos(x)$ is the first line

6. anonymous

you made a mistake in the second line

7. anonymous

sin (x-π/4)=sin x cos (–π/4)-cos x sin( –π/4) should be sin (x-π/4)=sin x cos (π/4)-cos x sin( π/4)

8. anonymous

Yea, you're right I made a mistake with the - sign. How would I go about finding the solution?

9. anonymous

hmm now that i look more carefully, ;perhaps you get $\sqrt{2}\sin(x)$ when you add

10. anonymous

no matter, now solve $\sqrt{2}\sin(x)=1$ which is the same as $\sin(x)=\frac{\sqrt2}{2}$

11. anonymous

pi/4 and 7pi/4 ?