Question

Помогите доказать эти тождестваsin (90°- α)=cos α; cos (90°- α)=sin α;

Answer 1

$sin(a-b) = sin(a)cos(b) - sin(b)cos(a)\\cos(a-b) = cos(a)cos(b) + sin(a)sin(b)\\sin(90-a) = sin(90)cos(a) - sin(a)cos(90) = 1 * cos(a) - sin(a) * 0 = cos(a)\\cos(90-a) = cos(90)cos(a) + sin(90)sin(a) = 0*cos(a) + 1 * sin(a) = sin(a)$