I need help solving both problems. Can someone please solve them? Thanks

Let cosx=y

cos2x+cosx= 2y^2+y-1=f(y) suchthat y lies in -1 to 1.

Now find f(1), f(-1) and then differentiate f(y) and set it to zero to obtain y=-1/4. Find f(-1/4). Compare these three values and the least one of them is the minimum value.

For the first question, write sin^2x and cos^2x in terms of cos2x and sinx-cosx as sin2x/2 and then set 2x=y. Having done this, use the fact that asinx+bcosx lies in -√(a^2+b^2) to √(a^2+b^2).