3sin^2x + 4sinxcosx + 5cos^2x = 2*1
3sin^2x + 4sinxcosx + 5cos^2x = 2*(sin^2x + cos^2x)
3sin^2x + 4sinxcosx + 5cos^2x = 2sin^2x + 2cos^2x
(3sin^2x - 2sin^2x) + 4sinxcosx + (5cos^2x - 2cos^2x)= 0
sin^2x + 4sinxcosx + 3cos^2x = 0 // : cos^2x ≠ 0
tg^2x + 4tgx + 3 = 0
tgx = t ==>
t^2 + 4t + 3 = 0
(t + 1)(t + 3) = 0
t = - 1 ;
t = - 3
tgx = - 1 ==> x = - pi/4 + pik, k ∈ Z
tgx = - 3 ==> x = - acrtg3 + pik, k ∈ Z
#2
3sin^2x + 4sinxcosx -7 cos^2x = 0 // : cos^2x ≠ 0
3tg^2x + 4tgx - 7 = 0
tgx = t ==>
3t^2 + 4t - 7 = 0
D = 16 + 4*3*7 = 100 = 10^2
t1 = ( - 4 + 10)/6 = 1
t2 = ( - 4 - 10)/6 = - 7/3
tgx = 1 ==> x = pi/4 + pik, k ∈ Z
tgx = - 7/3 ==> x = - arctg(7/3) + pik, k ∈ Z