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. [4T]

𝑠𝑖𝑛2
sin^2(𝑥) − √2𝑐𝑜𝑠(𝑥) = 𝑐𝑜𝑠^2 (𝑥) + √2𝑐𝑜𝑠(𝑥) + 2

see related problems below

hint: let u=cosx and things look a lot simpler.