10. -/1 points details my notes larat10 7.2 verify the identity. (simplify at each step.) 2 cos(π/2)…

Explanation:

Step1: Use co - function identities

Recall that $\cos(\frac{\pi}{2}-x)=\sin x$ and $\sin(\frac{\pi}{2}-x)=\cos x$. So, $\frac{2\cos(\frac{\pi}{2}-x)}{\sin(\frac{\pi}{2}-x)}=\frac{2\sin x}{\cos x}$.

Step2: Recall the definition of tangent

Since $\tan x=\frac{\sin x}{\cos x}$, then $\frac{2\sin x}{\cos x}=2\tan x$.

Answer:

The identity $\frac{2\cos(\frac{\pi}{2}-x)}{\sin(\frac{\pi}{2}-x)} = 2\tan x$ is verified. The missing expression in the middle step is $2\sin x$.