Chapter 14.1, Problem 28PPS

To determine

To find:The simplification of $\frac{1+{\text{sin}}^2\text{θ}}{{\text{sin}}^2\text{θ}}$

Answer to Problem 28PPS

  ${\text{cot}}^2\text{θ}$

Explanation of Solution

Given We know that the given expression is $\frac{1+{\text{sin}}^2\text{θ}}{{\text{sin}}^2\text{θ}}$

Calculation :

  $\begin{array}{l}\Rightarrow \frac{1+{\sin }^2\theta }{{\sin }^2\theta }\\ \because 1-{\sin }^2\theta ={\cos }^2\theta \\ \Rightarrow \frac{{\cos }^2\theta }{{\sin }^2\theta }\\ \Rightarrow {\left(\frac{\cos \theta }{\sin \theta }\right)}^2\\ \Rightarrow {\cot }^2\theta \end{array}$