Problem 25 - Precalculus Essentials

Question

Verify each identity. $$\frac{\sin t}{\csc t}+\frac{\cos t}{\sec t}=1$$

Step-by-Step Solution

Answer

After simplification, the equation becomes \(2\), not \(1\). There seems to be a mistake in the original exercise as this is not an identity.

Step 1: Change Reciprocal Trigonometric Identities

The first step in the problem is to replace the reciprocal trigonometric identities \(\csc t\) and \(\sec t\). The reciprocal of \(\csc t\) is \(\sin t\). Similarly, the reciprocal of \(\sec t\) is \(\cos t\). Thus, after replacing, the equation becomes: \(\frac{\sin t}{\sin t} + \frac{\cos t}{\cos t}\).

Step 2: Simplify the Equation

Here, both parts of the equation become: \(1 + 1\), since any number divided by itself equals to one.

Step 3: Sum the Units

Simply add the two ones together to get the simplified result: \(2\).