Please help I am supposed to verify that cot^2x+tan^2x =sec^2xcsc^2x-2

Question

I just can't seem to get the two equations to equal to each other.

Answer 1

two identities you should have in your bag of ID's is

csc^2 Ø -1 = cot^2 Ø , and
sec^2 Ø - 1 = tan^2 Ø

LS = left side
= csc^2 Ø - 1 + sec^2 Ø - 1
= csc^2Ø + sec^2 Ø - 2

= 1/sin^2 Ø + 1/cos^2 Ø - 2
= (cos^2 Ø + sin^2 Ø)/((sin^2 Ø)(cos^2 Ø)) - 2
= 1/((sin^2 Ø)(cos^2 Ø)) - 2
= csc^2 Ø sec^2 Ø - 2
= RS

At first it might seem that I was wrong, since we have the unusual result that
csc^2Ø + sec^2 Ø = csc^2 Ø sec^2 Ø
but I was able to show that this is true.