Question

Ex 27 va rog................ rezolvarea completă

Answer 1

Răspuns:

a) sin(2x)=m/2

daca -1 ≤ m/2 ≤ 1 ⇔ -2 ≤ m ≤ 2 ⇔ m ∈ [-2, 2] ⇒ 2x = arcsin(m/2) ⇒ x = 1/2·arcsin(m/2)

daca m ∈ (-∞,-2) ∪ (2,+∞) - ecuatia nu are solutii

b) √2cos(x)=m ⇔cos(x)= m/√2

daca -1 ≤ m/√2 ≤ 1 ⇔ -√2 ≤ m ≤ √2 ⇔ m ∈ [-√2, √2] ⇒ x = arccos(m/√2)

daca m ∈ (-∞,-√2) ∪ (√2,+∞) - ecuatia nu are solutii

c) tg(πx) = 1/m

m ≠ 0 ⇒ x = 1/π·arctg(1/m)

m = 0 - ecuatia nu are solutii