If $$cosec \ \theta = \frac{{5}}{3}$$​, then evaluate (sec²θ - 1) × cot²θ × (1 + cot²θ).

Correct option is C

Given:

$$cosec \ \theta =\frac{5}{3}$$​​

Formula Used:

​$$1 + \tan^2 \theta = \sec^2 \theta$$​​

​$$1 + \cot^2 \theta = \ cosec^2 \theta$$​

Solution:

​$$(\sec^2 \theta - 1) × \cot^2 \theta × (1 +\cot^2 \theta )$$​​

​$$\tan^2 \theta ×\cot^2 \theta × (1 +\cot^2 \theta )$$​​

​$$\frac{1}{\cot^2 \theta } ×\cot^2 \theta × \ cosec^2 \theta$$​​

​$$cosec^2 \theta$$​​

​$$(\frac{5}{3})^{2}$$​​

​$$=\frac{25}{9}$$​​