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
    
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