Question

2sinx + 1=tgx + 2sinxtgx

Answer 1

2sinx + 1 = tgx + 2sinxtgx
2sinx - 2sinxtgx + 1 - tgx = 0
2sinx(1 - tgx) + (1 - tgx) = 0
(2sinx + 1)(1 - tgx) = 0
2sinx = -1
sinx = -1/2
x = (-1)ⁿ+¹π/6 + πn, n ∈ Z
1 - tgx = 0
tgx = 1
x = π/4 + πn, n ∈ Z.