if someone could show me how to solve this problem

1) cos(345°)

did you notice that 345 = 360-15 ?

cos(345)
= cos15

cos15 = cos(45-30)
= cos45cos30 + sin45sin30
= (√2/2)(√3/2) + (√2/2)(1/2)
= ( √6 + √2)/4

cos 345 = (√6+√2)/4