I want to prove that $$\Gamma{(n)} \times \Gamma(n+\frac{1}{2}) = \sqrt{\pi} \times \Gamma(\frac{n}{2}) \frac{\sec(\frac{n\pi}{2})}{2^{1-n}}$$
What i know is the duplication formula which is $$\sqrt{\pi} \ \Gamma{(2n)} = \Gamma(n) \times \Gamma(n+\frac{1}{2})2^{2n-1}$$