Start me off for this trig equation (general solutions)

Question

dtan5457 · Answer

$$\sqrt{2} \cos x \sin x-cosx=0$$

dtan5457 · Answer

@matt101

matt101 · Answer

Try multiplying by the conjugate, then use the Pythagorean identity and see if that gets you anywhere

dtan5457 · Answer

I think I got it from factoring. To confirm, there should be 4 general solutions right? 2 from cos and 2 from sin

matt101 · Answer

Oh yes you're absolutely right! Here I am doing a way harder solution...

Yes, you'd most likely have 4 solutions (if your domain is +/- 2pi).

dtan5457 · Answer

No domain here, just general solutions

matt101 · Answer

Then yes

dtan5457 · Answer

I got.

cos=0=pi/2+2npi
3pi/2+2pin

sin(x)=pi/4+2npi
3pi/4+2npi

matt101 · Answer

Looks good!

I would just say that your solutions for cos and sin are actually the same (the second solution is just the first where n=1) so you might not need to include the second one for general solutions.

dtan5457 · Answer

I'll leave it JUST incase. Thanks, however.

matt101 · Answer

Haha not a a problem!