Question

If you start with a trigonometric expression and rewrite it or simplify it, then setting the original expression equal to the rewritten expression yields a trigonometric identity. For instance, from Example 1 we get the identity cos(t) +tan(t) sin(t)=sec(t) Use this technique to make up your own identity, then give it to a classmate to verify.

Answer 1

Using the double-angle formula, the trigonometric identity sin(2x) = 2sin(x)cos(x) can be derived and verified by substituting any angle for x to confirm that both sides of the equation match.

Step-by-step explanation:

To demonstrate the process of creating and verifying a trigonometric identity, let's work through an example. Take the trigonometric function sin(2x), which can be rewritten using the double-angle formula as 2sin(x)cos(x).

Setting the original expression equal to the rewritten one gives us the identity sin(2x) = 2sin(x)cos(x), a well-known trigonometric identity. To verify this, you can replace x with any angle and confirm that both sides of the equation will yield the same result. This method of creating identities applies to other trigonometric functions whereby applying formulas like angle addition, subtraction or double angle can lead to simplification and new identities.