trig identities: simplify cscX (1-cos^2X)(cotX), etc

[Pk designs]

Hi all,

I'm new to site and I kinda need little help, well actualy quite a bit of help ...

I have two expressions that I need to simplify, they're both separate expersions and not equal to each other but I'm getting stuck after converting them ... I havent taken or done trig in over 10yrs so theres alot of things I've just forgot, can someone please help me along { dont have to solve the work for me just a push in right direction} ...

problem one:

(csc X) (1-cos^2 X) (cot X)

now i've converted the above to simpler form...

(1/ sin X) (sin^2 X) (cos X)/ sin X)
and i dont know what to do next as far as combining them ...

problem two:
well it's sort of similar senerio ...

(csc X)(sec X - cosX)

converted to
(1/ sin X) ((1/ cos X) - cos)


know I'm suppose to combine the terms or reduce them to a simpler form but I'm not sure how to go about it either way ...
is there a reference chart, or link to a page that shows what expression reduces to what ...

any help given is greatly apricated

Thx in advance
Pete

 

[stapel]

It is usually a good strategy to convert everything to sines and cosines, and see where you can go from there.

1) csc(x) [1 - cos²(x)] cot(x)

The 1 - cos²(x) becomes sin²(x). The csc(x) becomes 1/sin(x). This gives you:

. . . . .[sin²(x) cos(x)] / [sin²(x)]

Cancel.

2) csc(x) [sec(x) - cos(x)]

The csc(x) becomes 1/sin(x); the sec(x) becomes 1/cos(x). Convert the terms in the square brackets to a common denominator, and combine. Convert the numerator using the Pythagorean Identity. Then cancel off the common factor of sin(x), and convert the resulting ratio into its equivalent trig function.

Eliz.

 

[Pk designs]

thank you so much you've been a great help