# Thread: solve the equation

1. ## solve the equation

sin x + cos x =1 [0,360 deg)

2. Originally Posted by dmak263
sin x + cos x =1 [0,360 deg)

$\sin(x) + \cos(x) = \sqrt{2} \sin(x+45)$

3. ## thanks

could you please explain the steps please...

4. Originally Posted by dmak263
could you please explain the steps please...
$A \sin x + B \cos x$ can always be written in the form $C \sin (x + \phi)$.

So expand $C \sin (x + \phi)$ and compare it with $A \sin x + B \cos x$ to get equations that you can use to solve for $C$ and $\phi$.

An alternative approach to solving the original equation is given here: Solving Equations Involving Cosine Plus Sine

Note that when using this approach you must always test the resulting solutions to see whether or not they satisfy the original equation.

5. thanks. I understand!!!