could you please solve for x this equation? sinx - cosx = 1`/sqrt(2)`

Expert Answers
embizze eNotes educator| Certified Educator

Solve `sinx-cosx=1/sqrt(2)` :

Square both sides (be aware that we might introduce extraneous solutions.):

`sin^2x-2sinxcosx+cos^2x=1/2` Use the Pythagorean relationship:



Use `sinucosv=1/2[sin(u+v)+sin(u-v)]`



`2x=pi/6,(5pi)/6,(13pi)/6,(17pi)/6` so


Checking we find that `x=pi/12,x=(17pi)/12` produce `-1/sqrt(2)` in the original equation so they are extraneous.


The solutions are `x=(5pi)/12+2npi,(13pi)/12+2npi` for `n in ZZ` (n an integer)


The graph:

aruv | Student




`because `








`x=npi+pi/4+(-1)^n(pi/6)`  and n is an integer.

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