Question

((csc y + cot y)(csc y - cot y))/csc y

Answer 1

the numerator is the difference of 2 squares....

so you have

\[\frac{\csc^2(y) - \cot^2(y)}{\csc(y)} = \frac{\csc^2(y)}{\csc(y)} - \frac{\cot^2(y)}{\csc(y)}\]

the fraction can be slip to allow for simplification

the 2nd term can be simplified by recognising

cot(y) = cos(y)/sin(y) and csc(y) = 1/sin(y)

Answer 2

oops should be split... not slip

Answer 3

so then what exactly will cancel out?

Answer 4

well the 1st fraction cancels to

\[\frac{\csc(y) \times \csc(y)}{\csc(y)} - \frac{\frac{(\cos^2(y)}{\sin^2(y)}}{\frac{1}{\sin(y)}}\]

cancel the common factor in the 1st term...

use the rule for dividing my negatives for the 2nd term

Answer 5

ok

Answer 6

oops you need to divide by a fraction... so flip the denominator and multiply


\[\csc(y) - \frac{\cos^2(y)}{\sin^2(y)} \times \frac{\sin(y)}{1}\]

Answer 7

so csc (y)- cos 2(y)/ sin (y) ?

Answer 8

yep.... that what it looks like to me..

Answer 9

then would i do 1/ sin (y)- cos 2 (y)/ sin (y)

Answer 10

you could that will make it as neat as possible...

Answer 11

ok, my answer choices are
-sin y
cos y
sin y
csc y

Answer 12

oops just realised... your step is correct...

and so you have

\[\frac{1 - \cos^2(y)}{\sin(y)} = \frac{\sin^2(y)}{\sin(y)}\]

still a step to go

Answer 13

oh, right

Answer 14

so sin y?

Answer 15

I used sin^2 + cos^2 = 1.... so sin^2 = 1 - cos^2

well done

Answer 16

yep... seems that way

Answer 17

sweet, thanks