Here's the problem:

2cos x + tan x= sec x

I changed the tan x into sin x/cos x

I changed the sec x into 1/cos x

Then I multiplied by cos x and then I factored. I got (2sin x + 3)(3sin x-1)=0

sin x = -3/2 and sin x = 1

But that's not the answer on the answer sheet. What did I do wrong?