Question

Find the exact values of all solutions in the interval 0=/< x<2pi for sin [x+(pi/4)] + sin [x-(pi/4)] = -1

Answer 1

do you know sin(a+b) and sin(a-b) formulae?

Answer 2

the product to sum formula?

Answer 3

or sum and difference?

Answer 4

sin(a+b)=sin a cos b+sin b cos a

Answer 5

oh yeah! i know that

Answer 6

sin(a-b)=sin a cosb-sin b cos a
so if you add sin(a+b) and sin(a-b) you're left with 2 sina cos b here a=x,b=pi/4 so 2sina/sqrt(2)=-1 sin a=-1/sqrt(2)

Answer 7

so you just use that formula to substitute? oh thanks! you're very helpful

Answer 8

yeah no problem.

Answer 9

sinxcospi/4 - cosxsinpi/4

Answer 10

sinxcospi/4 - cosxsinpi/4 = -1 what do i do next?

Answer 11

Expand both you have expanded only one two terms will cancel. You'll get sin x cos pi/4=-1 cos pi/4=sqrt(2)