Problem #6168 Complete the equation $csc(\theta) + 1 / cot(\theta) = \ldots$

Solution There can be various solutions. One of them is $csc\theta + 1 / cot\theta = \frac{1}{\sin\theta} + \frac{\sin\theta}{\cos\theta} = \frac{\cos\theta + \sin^2\theta}{\sin\theta\cos\theta} = (\cot\theta + \sin\theta)\frac{1}{\cos\theta} = (\cot\theta + 1 / csc\theta) \cdot sec\theta$.

Answer $csc(\theta) + 1 / cot(\theta) = (\cot \theta + 1 / csc\theta) \cdot sec\theta$.