Помогите пожалуйста 1) 2 sin (t+П/5) =корень 2 2) сos (2t +П/4)=0 3) tg(t/2- П/2) = - корень 3 4) сos^ 2(2t +П/6) = 1/2 5) ctg^ 2(2t - П/2)= 1/3 6) tg ^2 (3t+П/2)=1/3 7) 3 cos ^2 -5 cos t =0 8) !sin 3t! =1/2

1)  sin (t+П/5) =√2/2 t +π/5 = (-1)^n*arcsin(√2/2) + πn, n∈Z t +π/5 = (-1)^n*(π/4) + πn, n∈Z t = (-1)^n*(π/4) - π/5 + πn, n∈Z 2) сos (2t +П/4)=0 2t + π/4 =  π/2 + πk, k∈Z 2t  =  π/2 - π/4 + πk, k∈Z 2t  = π/4 + πk, k∈Z t  = π/8 + πk/2, k∈Z 3) tg(t/2- П/2) = - √3  - tg( π/2- t/2) = - √3  - ctg(t/2) = - √3   ctg(t/2) =  √3 t/2 = arctg(√3) + πn, n∈Z t/2 = π/3 + πn, n∈Z t = 2π/3 + 2πn, n∈Z 4) сos^ 2(2t + π/6) = 1/2   a)   сos(2t + π/6) = -√2/2 2t + π/6 = (+ -)*arccos(-√2/2) + 2πk, k∈Z  2t + π/6 = (+ -)*(π - π/4) + 2πk, k∈Z  2t + π/6 = (+ -)*(3π/4) + 2πk, k∈Z  2t  = (+ -)*(3π/4)  - π/6 + 2πk, k∈Z t1  = (+ -)*(3π/8)  - π/12 + πk, k∈Z b)   сos(2t + π/6) = √2/2 2t + π/6 = (+ -)*arccos(√2/2) + 2πk, k∈Z 2t + π/6 = (+ -)*(π/4) + 2πk, k∈Z 2t = (+ -)*(π/4) - π/6 + 2πk, k∈Z t2 = (+ -)*(π/8) - π/12 + πk, k∈Z 5) ctg^ 2(2t - П/2)= 1/3 a)  ctg(2t - П/2)= - √3/3 2t - π/2 = arcctg(-√3/3) + πn, n∈Z 2t - π/2 = 2π/3 + πn, n∈Z 2t  = 2π/3 + π/2+ πn, n∈Z 2t  = 7π/6 + πn, n∈Z t1  = 7π/12 + πn/2, n∈Z b)  ctg(2t - П/2)=  √3/3 2t - π/2 = arcctg(√3/3) + πn, n∈Z 2t - π/2 = π/3 + πk, n∈Z 2t  = π/3 + π/2+ πk, n∈Z 2t  = 5π/6 + πk, n∈Z t2  =5π/12 + πk/2, n∈Z 6) tg ^2 (3t+П/2)=1/3  a)  tg  (3t+π/2) = - √3/3 -ctg(3t)= -√3/3 ctg(3t)= √3/3 3t  = arcctg(√3/3) + πn, n∈Z 3t  = π/3 + πk, n∈Z t1  = π/9 + πk/3, n∈Z b)  tg  (3t+π/2) =  √3/3 ctg(3t)= - √3/3 3t  = arcctg(-√3/3) + πn, n∈Z 3t  = 2π/3 + πn, n∈Z t  = 2π/9 + πn/3, n∈Z 7) 3 cos ^2t - 5 cos t = 0 cost(3cost - 5) = 0 a)  cost = 0  t =  π/2 + πn, n∈Z b)  3cost - 5 = 0 cost = 5/3 не удовлетворяет условию: I cost I ≤ 1 8) !sin 3t! =1/2 a) sint = - 1/2 t = (-1)^(n)*arcsin( - 1/2) + πn, n∈Z t = (-1)^(n+1)*arcsin(1/2) + πn, n∈Z t1 = (-1)^(n+1)*(π/6) + πn, n∈Z b) sint = 1/2 t = (-1)^(n)*arcsin(1/2) + πn, n∈Z t2 = (-1)^(n)*(π/6) + πn, n∈Z