tanθcsc²θ - tanθ = cotθ

Explanation:

Step1: Factor out $\tan\theta$

$$\tan\theta(\csc^{2}\theta - 1)=\cot\theta$$

Step2: Use the Pythagorean identity $\csc^{2}\theta-1=\cot^{2}\theta$

$$\tan\theta\times\cot^{2}\theta=\cot\theta$$

Step3: Substitute $\tan\theta=\frac{1}{\cot\theta}$

$$\frac{1}{\cot\theta}\times\cot^{2}\theta=\cot\theta$$

Step4: Simplify the left - hand side

$$\cot\theta=\cot\theta$$

Answer:

The equation is an identity.