Answer
$$\cot\theta+\tan\theta=\sec\theta\csc\theta$$
The identity is proved to be true.
Work Step by Step
$$\cot\theta+\tan\theta=\sec\theta\csc\theta$$
We would try simplifying the left side first, using the identities $$\cot\theta=\frac{\cos\theta}{\sin\theta}$$ $$\tan\theta=\frac{\sin\theta}{\cos\theta}$$
The left side then would be $$\cot\theta+\tan\theta$$ $$=\frac{\cos\theta}{\sin\theta}+\frac{\sin\theta}{\cos\theta}$$ $$=\frac{\sin^2\theta+\cos^2\theta}{\sin\theta\cos\theta}$$ $$=\frac{1}{\sin\theta\cos\theta}$$ (for $\sin^2\theta+\cos^2\theta=1$) $$=\frac{1}{\sin\theta}\times\frac{1}{\cos\theta}$$ $$=\sec\theta\csc\theta$$ (we know that $\sec\theta=\frac{1}{\cos\theta}$ and $\csc\theta=\frac{1}{\sin\theta}$)
The identity is therefore proved.