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

Asked on by blehens

2 Answers | Add Yours

embizze's profile pic

embizze | High School Teacher | (Level 2) Educator Emeritus

Posted on

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's profile pic

aruv | High School Teacher | (Level 2) Valedictorian

Posted on




`because `








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

We’ve answered 319,865 questions. We can answer yours, too.

Ask a question