anonymous
  • anonymous
sin (x+(pi/4))-sin (x-(pi/4))=1 Help to solve for solutions?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • 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 \[\sqrt{2}\cos(x)\]
anonymous
  • anonymous
then it should be very easy you need to use the addition angle formula, and the subtraction angle formula for sine
anonymous
  • 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.

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anonymous
  • anonymous
some of those are numbers right?
anonymous
  • anonymous
\[\frac{\sqrt{2}}{2}\sin(x)+\frac{\sqrt{2}}{2}\cos(x)\] is the first line
anonymous
  • anonymous
you made a mistake in the second line
anonymous
  • 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)
anonymous
  • anonymous
Yea, you're right I made a mistake with the - sign. How would I go about finding the solution?
anonymous
  • anonymous
hmm now that i look more carefully, ;perhaps you get \[\sqrt{2}\sin(x)\] when you add
anonymous
  • anonymous
no matter, now solve \[\sqrt{2}\sin(x)=1\] which is the same as \[\sin(x)=\frac{\sqrt2}{2}\]
anonymous
  • anonymous
pi/4 and 7pi/4 ?

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