`sintheta-costheta = 1` Find the general solution.

2 Answers

embizze's profile pic

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

Posted on

Solve `sintheta-costheta=1` :

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


Use the Pythagorean identity and the double angle identity:




`theta=0,pi/2,pi,(3pi)/2` on `[0,2pi)`

Checking for extraneous solutions we find that only `theta=pi/2,theta=pi` are solutions. (`theta=0` gives `sin0-cos0=-1` and `theta=(3pi)/2` gives `sin(3pi)/2-cos(3pi)/2=-1` )


The general solution is `theta=pi/2 +2npi,theta=pi+2npi` ,`n in ZZ`



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aruv | High School Teacher | (Level 2) Valedictorian

Posted on











where n is an integer.It is general solution.

We have applied two formulas





So I have not cosider this .For cos(theta) there are two different value ,we need to choose unique .So I changed sin(theta).