Question

Hallar la cot de 105°conocidas las funciones de 60 y 45 grados xfa

Answer 1

cot 105° = cot (60 +45)

cotangente de la suma de dos angulos

cot (α+β) = (cotα .cotβ - 1)/cotβ +cotα

reemplazamos

cot (60 +45)

cot (60 +45) = (cot60 .cot45 - 1)/cot45 +cot60

cot (105) = (1/√3 .1 - 1)/(1 +1/√3)

cot 105 = (1/√3 -1)/(1 +1/√3)

cot 105 = (1/√3 -1)²/(1/√3 +1)(1/√3 -1)

cot 105 = (1/√3 -1)²/(1/3 -1)

cot 105 = (1/3 -2/√3 + 1)/-2/3

cot 105 = (4/3 -2/√3)/-2/3

cot 105 = - 3(4/3 -2/√3)/2

cot 105 = - 3(4/3 -2√3/3)/2

cot 105 = - (4 -2√3)/2

cot 105 = - (2 -√3)

cot 105 = - 2+√3