Please help me to solve the following equations (giving 1 or 2 solutions):

sin x = √3 cos x

sin^2x - cos^2x – sin x = 1

cos 2x + sin x + 1 = 0

sin 2 x + cos x = 0

tan^2x + sec x – 1 = 0

Any help no matter how little is much appreciated, I just don't know where to start.

Thanks in advance.