Q:

$\cos^2(\theta)-\sin^2(\theta)=1+\sin(\theta)$ over the interval $(0,2\pi)$

$\cos^2(\theta)-\sin^2(\theta)=1+\sin(\theta)$ over the interval $0<\theta<2\pi$
Find the trigonometric identity. 
Apologize for the confusion, first time using this resource didnt read the instructions.  i have tried manipulating the equation by substituting x^2 and y^2 in for the cos^2 and sin^2 and subtracting and adding the one but i could not find out what identities to use to make both side equal.  Sorry again for the mistake.  

A:

Hint: $\cos^2\theta - \sin^2\theta = 1-2\sin^2\theta$, so your equation becomes: $$2\sin^2\theta + \sin \theta = 0.$$

