Question

Verify (1-cot^2(w)+cos^2(w)*cot^2(w))/csc^2(w) = sin^4(w)

Answer 1

\[(1-\cot ^{2}(w) + \cos ^{2}(w)* \cot^2(w)) / \csc^2(w) = \sin^4(w)\]

Answer 2

[1-(cos^2w/sin^2w)+(cos^4w/sin^2w)]sin^2w=sin^2w-cos^2w+cos^4w

Answer 3

I got

\[\sin^2(w) - \cos^2(w) + \cos^4(w) = \sin^4(w)\]

but not sure where to go from here

Answer 4

does
\[\sin^2(w) - \cos^2(w) = -1??\]

Answer 5

no

Answer 6

are you sure the identity is correct?

Answer 7

yes

Answer 8

my homework problem in the book

Answer 9

my answer book looks like this:

\[(1-\cot^2(w)+\cos^2(w)\cot^2(w))/\csc^2(w)\]

down to:

\[(1-\cot^2(w)(1-\cos^2(w))/\csc^2(w)\]

but i'm not sure how

Answer 10

then

\[(1-\cot^2(w)\sin^2(w))/\csc^2\]

then:

\[(1-(\cos^2(w)/\sin^2(w))\sin^2(w))/\csc^2(w)\]

then

\[(1-\cos^2(w))/\csc^2(w)\]

then

\[\sin^2(w)/\csc^2(w)\]

to finally get

\[\sin^4(w)\]