Question

Use trigonometric identities to simplify the trigonometric expression:
(cscx+cotx)(cscx-cotx)

Answer 1

im assuming it starts out like this... csc^2x - cot^2x

Answer 2

hint:

(a+b)(a-b) = a^2 - b^2

Answer 3

good start, what's next?

Answer 4

yeah thats where im stuck=/

Answer 5

well one pythagorean identity is

1 + cot^2 = csc^2

and it's derived from the fact that sin^2 + cos^2 = 1

Answer 6

how can you manipulate that to get csc^2 - cot^2 ?

Answer 7

btw I found this (along with others) here

http://www.sosmath.com/trig/Trig5/trig5/trig5.html

Answer 8

if you move the cot^2 to the other side by subtraction..

Answer 9

good

Answer 10

so

1 + cot^2 = csc^2

1 + cot^2 - cot^2 = csc^2 - cot^2

1 = csc^2 - cot^2

Answer 11

oh, so the answer is 1?

Answer 12

yep

Answer 13

wow, that was easy! thanks again!!!

Answer 14

a very fancy way of saying 1 since it's always true for all of the defined values of x

Answer 15

yw

Answer 16

alright, got it!

Answer 17

oh and thanks for that link!!

Answer 18

sure thing, that is definitely very handy (since you aren't expected to memorize them all, at least I hope)

Answer 19

hah, yeah no way

Answer 20

you never know lol, but let's hope your teacher is understanding

Answer 21

god willing!