Доказать тождество (sinacosa)/ctga = 1 - (ctg^2a - cos^2a)/ctg^2a

(sinacosa)/ctga = 1 - (ctg²a - cos²a)/ctg²a (sinacosa)/(cosa/sina) = (ctg²a - ctg²a   + cos²a)/ctg²a sin²acosa/cosa = cos²a/ctg²a sin²a = cos²a/(cos²a/sin²a) sin²a = cos²asin²a/cos²a sin²a = sin²a

(sinacosa)/ctga = 1 - (ctg^2a - cos^2a)/ctg^2asinacosa/ctga=sinacosa: cosa/sina=sinacosa*sina/cosa=sin²a 1 - (ctg^2a - cos^2a)/ctg^2a=1-(cos²a/sin²a-cos²a): cos²a/sin²a= =1-cos²a(1-sin²a)/sin²a *sin²a/cos²a=1-1+sin²a=sin²a sin²a=sin²a

по теореме пифагора найдём вс:

25-16=9=3

синус а= 3/5