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Homework Statement
cot^{2}x + sec^{2}x = tan^{2}x + csc^{2}x
Homework Equations
The Attempt at a Solution
I began by working on my left side.
I got up until
=cos^4x + sin^2x / sin^2x cos^2x
And unsure of where to go next.
You made a good start working on the LHS. Do the same to the RHS and see what you get.Homework Statement
cot^{2}x + sec^{2}x = tan^{2}x + csc^{2}x
Homework Equations
The Attempt at a Solution
I began by working on my left side.
I got up until
=cos^4x + sin^2x / sin^2x cos^2x
And unsure of where to go next.
On right side I got sin^4x + cos^2x / cos^2x sin^2x , I can't seem to get itYou made a good start working on the LHS. Do the same to the RHS and see what you get.
Compare the LHS to the RHS now. Do you notice anything in common?On right side I got sin^4x + cos^2x / cos^2x sin^2x , I can't seem to get it
L.S = cos^4x / sin^2x cos^2x + sin^2x / sin^2x cos^2xCompare the LHS to the RHS now. Do you notice anything in common?
I'm having a problem seeing how you go from the expression above to the one below:L.S = cos^4x / sin^2x cos^2x + sin^2x / sin^2x cos^2x
= cos^2x / sin^2x + 1 / cos^2x
I see that you found the common denominator, but your numerator is incorrect.= cos^2x + sin^2x / sin^2x cos^2x
Same comments from the LHS calculations apply above.= 1 / sin^2x cos^2x
R.S = sin^4x / sin^2x cos^2x + cos^2x / sin^2x cos^2x
= sin^2x / cos^2x + 1 / sin^2x
= sin^2x + cos^2x / sin^2x cos^2x
= 1 / sin^2x cos^2x
Would this be the answer?
On right side I got sin^4x + cos^2x / cos^2x sin^2x
When writing "fractions" with an "in-line" format, one using the " / " character, you need to use parentheses to include (the entire numerator) / (the entire denominator).L.S = cos^4x / (sin^2x cos^2x) + sin^2x / (sin^2x cos^2x)
= cos^2x / sin^2x + 1 / cos^2x
= ( ? × cos^2x + sin^2x) / (sin^2x cos^2x)
= 1 / (sin^2x cos^2x)
R.S = sin^4x / (sin^2x cos^2x) + cos^2x / (sin^2x cos^2x)
= sin^2x / cos^2x + 1 / sin^2x ( No idea what you did here. Whatever, it's not legal.)
= (sin^2x + cos^2x) / (sin^2x cos^2x)
= 1 / (sin^2x cos^2x)
Would this be the answer?