Докажите тождество

cos (2a+п) = cos^2 (a-п/2) + cos (a+п) sin (a+п/2)

Cos (2α+π) = cos² (α-π/2) + cos (α+π) ·sin (α+π/2); ⇒

cos (2α+π) = - cos2α;

cos² (α-π/2) + cos (α+π) ·sin (α+π/2) = cos² ( - (π/2-α)) - cosα·cosα=

=sin²α-cos²α=-cos2α; ⇒

-cos2α=-cos2α;