a) cos(a-b) - cos(a+b) = cos(a)*cos(b) + sin(a)*sin(b) - (cos(a)*cos(b) - sin(a)*sin(b)) = cos(a)*cos(b) + sin(a)*sin(b) - cos(a)*cos(b) + sin(a)*sin(b) = 2sin(a)*sin(b)

b) sin(2a) + cos(2a) + 1 = 2*sin(a)*cos(a) + cos²(a) - sin²(a) + cos²(a) + sin²(a) = 2*sin(a)*cos(a) + 2*cos²(a) = 2*cos(a)*(sin(a) + cos(a))

sin() = -

= arcsin(-) + 2πκ, κ∈Ζ

или

= π - arcsin(-) + 2πn, n∈Ζ

= - + 2πκ, κ∈Ζ

= π + + 2πn, n∈Ζ

= + 2πn, n∈Ζ

x₁ = - + 6πκ, κ∈Ζ

x₂ = + 6πn, n∈Ζ

Отбор корней произведем с помощью неравенств.

x₁: 0 ≤  - + 6πκ ≤ 3π

≤ 6πκ ≤ 3π +

≤ 6πκ ≤

≤ 6κ ≤

≤ κ ≤

Так как κ∈Ζ, то  κ∈∅

x₂: 0 ≤   + 6πn ≤ 3π

- ≤  6πn ≤ 3π -

- ≤  6πn ≤ -

- ≤  6n ≤ -

- ≤  n ≤ -

Так как n∈Ζ, то  n∈∅ ⇒ нет корней на данном промежутке