Thread: Please help with these Algebra questions

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.

Hints:
1) divide by cos(x) both sides

2) subtract 1 on both sides then use the equality cos^2(x)=1-sin^(x)

3) cos(2x)=cos^2(x)-sin^2(x) and 1=sin^2(x)+cos^2(x)

4) sin(2x)=2sin(x)cos(x)

5) tan^2(x)=sec^2(x)+1

1) divide by cos(x) both sides

2) subtract 1 on both sides then use the equality cos^2(x)=1-sin^2(x)

3) cos(2x)=cos^2(x)-sin^2(x) and 1=sin^2(x)+cos^2(x)

4) sin(2x)=2sin(x)cos(x)

5) tan^2(x)=sec^2(x)+1

I just fix something I think you need to clear.