Precal Trigonometry (please help)

Question

Verify the identity.

csc(x)-cot(x)=1/[csc(x)+cot(x)]

Thank you!

Answer 1

Hi Kayla.

Start with the Pythagorean Identity that csc²A - cot²A = 1

Remember back in Algebra, a² - b² = (a - b)(a +b)

Well that is true of csc²A - cot²A = (cscA - cotA)(cscA + cotA)

Knowing this, if we work down the Right side, multiply top and bottom by [cscX - cotX]

This gives

1 · [cscX - cotX]

-----------------------

(cscX + cotX) [cscX - cotX]

the top now is just [cscX - cotX]

and the bottom now is csc²X- cot²X = 1

Now we have

[cscX - cotX]

-----------------

1

= [cscX - cotX]

and it is verified!

(I am available today for online tutoring if you are interested... rate = $55/hour)