Question

PRECALC HELP PLEASE!!!
Verify: csc^2xcot^2x + csc^2x = csc^4x

Answer 1

@TheSmartOne

Answer 2

i think we can use the identity

csx^2 x = 1 + cot^2 x

Answer 3

from this cot^2 x = csc^2 x - 1

plug this into the left side of the identity and simplify.

Answer 4

So change all the csc to 1+cot^2x ?

Answer 5

No change the cot^2 x to csc^2 x - 1

Answer 6

So then would the exponents multiply in in the first part?

Answer 7

so

csc^2 x ( csc^2 x - 1) + csc^2 x

Simplify this and see what you get.

Answer 8

when you multiply you add exponents

Answer 9

its now easy to solve.

Answer 10

So right now I have csc^4x - 1 + csc^2x

Answer 11

Am I on the right track?

Answer 12

you made 1 mistake
csc^2 x is distributed over every term in the parentheses.

Answer 13

OH! So the last 2 terms cancle!

Answer 14

you did csc^2 x + csc^2 x = csc^4 x

but also its csc^2 x * -1

Answer 15

yes they cancel leaving just csc^4 x

Answer 16

Thank you so much!

Answer 17

yw