How do you solve $cosx + 1 = sinx$ ?

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Answer 1 · 2015-04-16T14:57:42

This is a linear equation is sinus and cosine.

The faster way, to solve it, is this:

$sinx-cosx=1$ let's multiply all the members with $sqrt2/2$

$sinx*sqrt2/2-cosx*sqrt2/2=sqrt2/2$ and the first member is the development of: $sin(x-pi/4)$ , so:

$sin(x-pi/4)=sqrt2/2rArr$

$x-pi/4=pi/4+2kpirArrx=pi/2+2kpi$

and

$x-pi/4=3/4pi+2kpirArrx=pi+2kpi$ .

How do you solve cosx + 1 = sinxcosx + 1 = sinx?