# Thread: What identities prove this statement is correct?

1. ## What identities prove this statement is correct?

1 – cos2x/(1 + Sinx) = Sinx?

Thank you!

2. ## Re: What identities prove this statement is correct?

Is that \displaystyle \displaystyle \begin{align*} 1 - \frac{\cos^2{x}}{1 + \sin{x}} \end{align*}?

3. ## Re: What identities prove this statement is correct?

That is a great question. I believe it is. I am taking an online pre-calc class and that is exactly how the question appears. The professor is not too helpful......He said this statement is true so i do think it is how you noted. Any help would be greatly appreciated

4. ## Re: What identities prove this statement is correct?

Originally Posted by DanielleNY
That is a great question. I believe it is. I am taking an online pre-calc class and that is exactly how the question appears. The professor is not too helpful......He said this statement is true so i do think it is how you noted. Any help would be greatly appreciated
\displaystyle \displaystyle \begin{align*} 1 - \frac{\cos^2{x}}{1 + \sin{x}} &\equiv 1 - \frac{1 - \sin^2{x}}{1 + \sin{x}} \\ &\equiv 1 - \frac{\left(1 - \sin{x}\right)\left(1 + \sin{x}\right)}{1 + \sin{x}} \\ &\equiv 1 - \left(1 - \sin{x}\right) \\ &\equiv 1 - 1 + \sin{x} \\ &\equiv \sin{x} \end{align*}

5. ## Re: What identities prove this statement is correct?

wow thank you so much for the quick reply!!!...I will definitely be visiting this forum a lot more