Trig Identity clarification

Question

The question is: sin theta = cos (theta + 10)

For my answers I got

1. theta = 90^o - (theta + 10^o) + 360^on : [180^o(9n +2)]/9
2. theta = 180^o - (90^o - (theta + 10^o)) = 360^on

For the second I found it's true for all theta; 0 = 180^o - 80^o +360^on, but only the first answer is correct. I was just wondering why only the first is right if the second is also true? Could someone please clarify the interpretations of these answers? thanks :)

Answer 1

Are you sure that's the problem? Just a statement, or is there more?