Chapter 5.1, Problem 118E

Prove that the following inequalities are true for $0<\theta <\frac{\pi }{2}$ .

a. ${\sin }^2\theta +{\csc }^2\theta \ge 2$

b. ${\cos }^2\theta +{\sec }^2\theta \ge 2$

c. ${\sec }^2\theta +{\csc }^2\theta \ge 4$