Step by step
The question
Question: simplify cos x × sec x.
Simplify means: write it as simply as we can.
cos x × sec x
1 Write in sin and cos
Everything is easier in sin and cos.
sec is 1 over cos.
sec x = 1cos x
We put them in.
Tops go on top, bottoms at the bottom.
= cos xcos x
2 Cancel
Now we look for the same thing on top and at the bottom.
= cos xcos x
Careful!
sin x means the sine of x.
It is one thing.
We cross out a whole sin x, never the x alone.
Careful: sin x is one thing
Every cos x on top has a partner at the bottom.
Each pair over itself is 1.
Cross them out.
What is left: 1.
= 1
So it simplifies to 1.
3 Check
Let's check with a number: x = 30°.
On the calculator, cos 30° × sec 30° is about 1.0000.
x = 30°: cos 30° × sec 30° ≈ 1.0000
Our answer is 1.
The same!
So it is right.
answer: 1
Let's look back.
First: write in sin and cos.
Then: cancel.
Last: check.
Answer
= 1