If sinx + sin 2 8 4 x = 1 then cos x + 2cosx + cosx is equal to

To solve the equation sinx + sin 2 8 4 x = 1, we can start by simplifying the equation.

Let's rewrite sin 2 8 4 x as sin(2x) and cos x + 2cosx + cosx as 4cosx.

So, the equation becomes sinx + sin(2x) = 1.

Next, we can use the double angle formula for sine, which states that sin(2x) = 2sinx*cosx.

Substituting this into the equation, we get sinx + 2sinx*cosx = 1.

Now, we can factor out sinx from the left side of the equation: sinx(1 + 2cosx) = 1.

To solve for cosx, we divide both sides of the equation by sinx: 1 + 2cosx = 1/sinx.

Simplifying further, we have 2cosx = 1/sinx - 1.

Finally, we can divide both sides of the equation by 2 to isolate cosx: cosx = (1/sinx - 1)/2.

So, cos x + 2cosx + cosx is equal to 4cosx, which can be substituted with 4[(1/sinx - 1)/2].