# Solve Linear Trig Equations

1. Nov 24, 2016

### Veronica_Oles

1. The problem statement, all variables and given/known data
Solve sin (x + pi/4) = √2 cos x

2. Relevant equations

3. The attempt at a solution
sinx*cos(pi/4) + cosx*sin(pi/4) = √2 cos x
√2/2 sinx + √2/2 cosx = √2 cos x
not sure if im on the right track? or where would I go from here? would I bring √2 cos x to the left side?

2. Nov 24, 2016

### LCKurtz

I would note that $\frac {\sqrt 2} 2 = \frac 1 {\sqrt 2}$ and multiply both sides by $\sqrt 2$.

3. Nov 24, 2016

### Veronica_Oles

Did that now I'm left with (sinx + cosx) = 2cosx, I'm stuck now? Tried bringing to other side and does not work and tried cancelling out the cosx but that does not work.

4. Nov 24, 2016

### LCKurtz

Show us what you get when you simplify it. Telling us it didn't work doesn't help us help you when we don't know what you did.

5. Nov 24, 2016

### lurflurf

just use the identity
$$\sin\left(x+\frac{\pi}{4}\right)=\sin\left(x-\frac{\pi}{4}\right)+\sqrt{2}\cos(x)$$
or equivalently
$$\sin\left(x+\frac{\pi}{4}\right)-\sin\left(x-\frac{\pi}{4}\right)=\sqrt{2}\cos(x)$$

6. Nov 24, 2016

### Veronica_Oles

(sinx + cosx)/cosx = (2cosx)/cosx

Now I am left with

(sinx/cosx) + 1 = 2

sinx/cosx = 2-1

tanx = 1

x = tan-1(1)

x = pi/4

or

x = pi + pi/4 = 5pi/4

7. Nov 24, 2016

### LCKurtz

How about angles coterminal with those?