Proving Identities:

Question

2 columns
(tan + cot)^2 = sec^2 + csc^2
I'm having trouble breaking down the left side to = the right side..
Any help please

Answer 1

left
(sin/cos + cos/sin)^2

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

right
1/cos^2 + 1/sin^2

sin ^2/cos^2sin^2 + cos^2/cos^2 sin^2

1/cos^2 sin^2

Answer 2

Hi Damon .. apparently they want the right side to stay "as is" and for the left side to transform into exactly what the right side says .... sorry

Answer 3

I do not think so. That would be a very unusual thing for "them" to say :)

Answer 4

The question says: Set up a 2 column proof to show that each of the following equations is an identity. Transform the left side to become the right side.
(tan + cot)^2 = sec^2 + csc^2

Answer 5

(tan + cot)^2 = tan^2 + 1 + cot^2
= sec^2 - 1 + 2 + csc^2 - 1
= sec^2 + csc^2

Answer 6

oops that's tan^2 + 2 + cot^2