Question

вычислите ctg 38*ctg 22/ctg38+ctg22. решите пожалуйста!!!! очень надо сегодня

Answer 1

$frac{ctg38cdot ctg22}{ctg38+ctg22} = frac{frac{cos38}{sin38}cdot frac{cos22}{sin22} }{ frac{cos38}{sin38} + frac{cos22}{sin22} } = frac{cos38cdot cos22cdot ; sin38cdot sin22}{sin38cdot sin22cdot (sin22cdot cos38+cos22cdot sin38)} =\\= frac{cos38cdot cos22}{sin(22+38)} = frac{frac{1}{2}cdot (cos(38+22)+cos(38-22))}{sin60} =\\= frac{frac{1}{2}cdot(cos60+cos16)}{sqrt3/2} = frac{frac{1}{2}+cos16}{sqrt3} =frac{1+2cos16}{2sqrt3}= frac{sqrt3(1+2cos16)}{6}$