(5sinx - 12cosx)^2 = 13^2
25sin^2x - 120sinxcosx + 144cos^2x = 169sin^2x + 169cos^2x
- 144sin^2x - 120sinxcosx - 25cos^2x = 0 /:(-1)
144sin^2x + 120sincosx + 25cos^2x = 0
(12 sinx + 5cosx)^2 = 0
12sinx + 5cosx = 0 /:cosx ≠ 0
12tgx + 5 = 0
12tgx = - 5
tgx = - 5/12
x = - arctg(5/12) + pik, k ∈Z