Solve the following equation and state the general solution for all values of x in exact form. Show all

steps of your algebraic solution for full marks

𝑠𝑖𝑛^2(𝑥) − √2𝑐𝑜𝑠(𝑥) = 𝑐𝑜𝑠*2(𝑥) + √2𝑐𝑜𝑠(𝑥) + 2

let u = cos(x)

and then solve
2u^2 - 2√2 u + 1 = 0

this problem has come up already a few times here.
too bad the search box is virtually useless on this site. :-(