Question

prove that
cosec^4 x - cosec^2 x = cot^2 x + cot^4 x

Answer 1

you know the pythagorean identity involving cot^2 and cosec^2 ?

Answer 2

i don't know

Answer 3

do you know ANY pythagorean identity ?

Answer 4

sin^2x + cos^2x =1
1 + tan^2x=sec^2x

Answer 5

and the last one is
\(1+ \cot^2 x = cosec^2x\)

from
cosec^4 x -cosec^2 x

factor out cosec^2 x
what do u get ?

Answer 6

cosec^2 x * cot^2 x

Answer 7

thats correct!
now replace that cosec^2 x as 1+cot^2 x and muliply the terms , and you will get your result :)

Answer 8

thx for help

Answer 9

i got it

Answer 10

welcome ^_^