Asked by Don
Proving Identities:
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
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
Answers
Answered by
Damon
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
(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
Answered by
Don
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
Answered by
Damon
I do not think so. That would be a very unusual thing for "them" to say :)
Answered by
Don
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
(tan + cot)^2 = sec^2 + csc^2
Answered by
Steve
(tan + cot)^2 = tan^2 + 1 + cot^2
= sec^2 - 1 + 2 + csc^2 - 1
= sec^2 + csc^2
= sec^2 - 1 + 2 + csc^2 - 1
= sec^2 + csc^2
Answered by
Steve
oops that's tan^2 + 2 + cot^2