Question

Sin 2х + 2cosx= sinx+1 решите тригонометрические уравнивание различных типов

Answer 1

2sinxcosx+2cosx=2cosx(sinx+1)
2coax(sinx+1)=sinx+1
(sinx+1)(2cosx-1)=0
sinx=-1 ; x=-pi/2+2pik
2cosx=1; cosx=1/2; x=+-pi/3+2pik

Answer 2

This equation looks like a bit of a challenge, but let's tackle it together. The equation is $\sin(2x) + 2\cos(x) = \sin(x) + 1$, right?

First, let's simplify it a bit. We can use the double angle identity for sine, which is $\sin(2x) = 2\sin(x)\cos(x)$:

$2\sin(x)\cos(x) + 2\cos(x) = \sin(x) + 1$

Now, let's gather all the terms on one side:

$2\sin(x)\cos(x) - \sin(x) - 2\cos(x) + 1 = 0$

Now, let's see if we can factor this expression. It seems a bit tricky, so we might need to use some substitution or identities. Does any particular approach come to mind for you?