Chapter 14.1, Problem 30PPS

To determine

To find:Simplification of $\frac{1}{{\text{sin}}^2\text{θ}}-\frac{{\text{cos}}^2\text{θ}}{{\text{sin}}^2\text{θ}}$

Answer to Problem 30PPS

  $\text{1}$

Explanation of Solution

Calculation :

  $\begin{array}{l}\Rightarrow \frac{1}{{\text{sin}}^2\text{θ}}-\frac{{\text{cos}}^2\text{θ}}{{\text{sin}}^2\text{θ}}\\ \Rightarrow \frac{\text{1}-{\text{cos}}^2\text{θ}}{{\text{sin}}^2\text{θ}}\\ \because 1-{\text{cos}}^2{\text{θ=sin}}^2\text{θ}\\ \Rightarrow \frac{{\text{sin}}^2\text{θ}}{{\text{sin}}^2\text{θ}}\\ \Rightarrow 1\end{array}$