Question

Urgenteeee ayudenme con la respuesta!!!!

Answer 1

Solución:

tg α = (2cos 45° + tg 45°) / (csc 45° - ctg 45°)

Utilizar triangulo notable de 45°:
tg α = (2(1 / √2) + 1) / (√2 - 1)
tg α = (2 / √2 + 1) / (√2 - 1)
tg α = (2√2 / (√2√2)  + 1) / (√2 - 1)
tg α = (2√2 / 2 + 1) / (√2 - 1)
tg α = (√2 + 1) / (√2 - 1)
tg α = (√2 + 1)(√2 + 1) / ((√2 - 1)(√2 + 1))
tg α = (√2 + 1)² / (√2² - 1²)
tg α = (√2 + 1)² / (2 - 1)
tg α = (√2 + 1)² / 1
tg α = (√2 + 1)² 
tg α = √2² + 2(√2)(1) + 1² 
tg α = 2 + 2√2 + 1 
tg α = 3 + 2√2

cateto opuesto = 3 + 2√2
cateto adyacente = 1
hipotenusa = x

Utilizar teorema de pitagoras:
x² = (3 + 2√2)² + 1²
x² = 3² + 2(3)(2√2) + (2√2)² + 1
x² = 9 + 12√2 + 4√2² + 1
x² = 9 + 12√2 + 4(2) + 1
x² = 9 + 12√2 + 8 + 1
x² = 18 + 12√2 
x =√(18 + 12√2)

M = sen α . cos α
M = ((3 + 2√2) / √(18 + 12√2))(1 / √(18 + 12√2))
M = (3 + 2√2) / √(18 + 12√2)²
M = (3 + 2√2) / (18 + 12√2)
M = (3 + 2√2) / (6(3 + 2√2))

M = 1 / 6