Question

please help. 1. sin x (csc(x)-sin (x))
2. (1-cot^2(x))(1-cos^2(x))
3. 1-tan^2(x) / sec^2(x)
I have to simplify them but I'm not sure how

Answer 1

So
csc(x) is the same as 1/sin(x)
cot(x) is the same as 1/tan(x)
sec(x) is the same as 1/cos(x)
tan(x) is the same as sin(x)/cos(x)

Now that that is out of the way, there is a rule that sin^2(x) + cos^2(x) = 1

This equation can be changed to
cos^2(x) = 1 - sin^2(x)
or
sin^2(x) = 1 - cos^2(x)

You can also get two other equations out of this by dividing both sides by by sin^2(x) and cos^2(x)

By dividing both sides by cos^2(x) you get
sin^2(x)/cos^2(x) + 1 = 1/cos^2(x)
This can be simplified to
tan^2(x) +1 = sec^2(x)

By dividing both sides by sin^2(x) you get
1 + cos^2(x)/sin^2(x) = 1/sin^2(x)
This can be simplified to
1 + cot^2(x) = csc^2(x)

I'm too lazy to do the rest but hopefully this helped with your problem.

Answer 2

yeah it did. thanks a lot (: