Express sin⁡θ in terms of cot⁡θ, where θ is an acute angle.

Given: 

​$$\theta$$ is acute angle;

To express $$\sin \theta$$ in terms of $$\cot \theta$$ 

Formula Used: 

​$$\cot \theta = \frac{\cos \theta}{\sin \theta}$$ 

​$$\sin^2 \theta + \cos^ 2\theta = 1$$ 

Solution: 

​$$\cot \theta = \frac{\cos \theta}{\sin \theta} \implies \cos \theta = \sin \theta \cdot \cot \theta$$ 

Now, 

​$$\sin^2 \theta + \cos^ 2\theta = 1 \\ \ \\ \sin^2 \theta + (\sin \theta \cdot \cot \theta)^2 = 1 \\ \ \\ \sin^2 \theta ( 1+ \cot^2 \theta) = 1 \\ \ \\ \sin^2 \theta = \frac{1}{1 + \cot^2 \theta} \\ \ \\ \implies \bf \sin \theta = \frac{1}{\sqrt{1 + \cot^2 \theta}}$$​​​​