Question

как доказать тождество (ctg t )/(tg t+ctg t) = cos^2 t

Answer 1

$frac{ctgt}{tgt+ctgt} = frac{frac{cost}{sint}}{frac{sint}{cost}+frac{cost}{sint}} = frac{cost}{sintcdot frac{sin^2t+cos^2t}{sintcdot cost}} = frac{cost}{frac{1}{cost}} =cos^2t$