Question

2sin 2 x + 6sin 2x = 7(1 + cos 2x)

Answer 1

2sin(2x) + 6sin(2x) = 7(1+cos(2x))
2sin(2x) + 6 sin(2x) = 7+7cos(2x)
8sin(2x)=7sin²x+7cos²x +7cos²x - 7sin²x
8sin(2x)= 14cos²x
16(sinx)*cos(x)-14cos²x=0
2cos (x) (8sin(x)-7cos(x))=0
cos(x)=0
x=π/2 + πn, n ∈ Z
8sin(x)-7cos(x)=0
8tg(x)-7=0
tg(x)=7/8
x=arctg(7/8) + πn, n  ∈ Z