Algebra and Trigonometry 10th Edition

$\theta=\dfrac{(2n+1)\pi}{2}$
Our aim is to prove that $\theta=\dfrac{(2n+1)\pi}{2}$ Let us suppose that $\theta$ is an angle such that $\cos \theta =0$. Recall that any odd multiple of $\dfrac{\pi}{2}$ satisfies the equation $\cos \theta =0$. This implies that $\theta=(a)(\dfrac{\pi}{2})$ for any odd integer $a$ would also satisfy the equation $\cos \theta =0$. So, we can write this as: $\theta=(a)(\dfrac{\pi}{2}) \implies \theta=(2n+1)(\dfrac{\pi}{2})$ Thus the result has been proven: $\theta=\dfrac{(2n+1)\pi}{2}$