WEBVTT

1
00:00:00.000 --> 00:00:03.831
Here is the problem: sin(x) squared plus cos(x) squared.

2
00:00:04.281 --> 00:00:06.568
Simplify a trigonometric expression.

3
00:00:07.368 --> 00:00:13.928
Rewrite everything in terms of sin x and cos x. The expression already uses only sine and cosine.

4
00:00:14.378 --> 00:00:16.270
Combine into a single fraction.

5
00:00:16.720 --> 00:00:24.742
Use sin squaredx plus cos squaredx equals 1 (replace cos squared with 1 minus sin squared) and cancel common factors.

6
00:00:25.542 --> 00:00:26.993
So the answer is 1.

7
00:00:27.443 --> 00:00:34.804
sin(x) squared plus cos(x) squared simplifies to 1 for every x where the original expression is defined.

8
00:00:35.604 --> 00:00:41.351
Numeric spot check: the original expression and the result agree at sample values of x.