jika x1 dan x2 adalah solusi dari persamaan (2sinxcos2x/cosxsin2x) - 5tanx +5 =0, maka tan(x1+x2)?

(2sinxcos2x/cosxsin2x) - 5tanx + 5 = 0
[2sinx(1-2sin²x)/cosx(2sinxcosx)] - 5tanx + 5 = 0
(1-2sin²x)/cos²x - 5tanx + 5 = 0
(1-sin²x-sin²x)/cos²x - 5tanx + 5 = 0
(cos²x-sin²x)/cos²x - 5tanx + 5 = 0
1 - tan²x - 5tanx + 5 = 0
tan²x + 5tanx - 6 = 0

misalkan tanx = m
m² + 5m - 6 = 0
(m+6)(m-1) = 0
m1 = -6 m2 = 1
tanx1 = -6 tanx2 = 1

tentukan tan(x1+x2)
= (tanx1 + tanx2)/(1-tanx1tanx2)
= (-6 + 1)/(1 -(-6)(1))
= -5/7