Question

Find the exact value of each expression. Do not use a calculator.

$\csc \frac{\pi }{2}+\cot \frac{\pi }{2}$

Short answer

The exact value of the given expression is 1.

Step-by-step solution

Step 1. Given information.

The given expression is:

$\csc \frac{\pi }{2}+\cot \frac{\pi }{2}$

Step 2. Determine the exact value.

In the trigonometric table $\csc \frac{\pi }{2}=1$and $\cot \frac{\pi }{2}=0$. Substitute these values in the given expression.

$\begin{array}{rcl}\csc \frac{\pi }{2}+\cot \frac{\pi }{2}& =& \left(1\right)+\left(0\right)\\ & =& 1\end{array}$

Step 3. Conclusion.

The exact value of the given expression is 1.