Question

sin (x+(pi/4))-sin (x-(pi/4))=1
Help to solve for solutions?

Answer 1

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
\[\sqrt{2}\cos(x)\]

Answer 2

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

Answer 3

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.

Answer 4

some of those are numbers right?

Answer 5

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

Answer 6

you made a mistake in the second line

Answer 7

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)

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

pi/4 and 7pi/4 ?