Question

Please help me complete these identities:
1) cscx cotx / secx
2) sec^2x csc^2x

Answer 1

rewrite all in terms of sine and cosine and it will be much easier

Answer 2

I did and I'm stuck...
1) (1/sinx 1/tanx)/ 1/cosx
2) 1/cos^2x (1/sin^2x)
Where do I go from here?
I've been up most of the night working on this kind of problems and my brain is beyond fried.

Answer 3

lets replace cosine by \(a\) and sine by \(b\)
then the first one is
\[\frac{\frac{1}{b}\times \frac{b}{a}}{\frac{1}{a}}\]

Answer 4

nothing left but algebra
you get
\[\frac{b}{ab}\times \frac{a}{1}\]
\[=\frac{ab}{ab}=1\]

Answer 5

oh damn i made a mistake, scratch that

Answer 6

you actually get
\[\frac{\frac{1}{b}\times \frac{a}{b}}{\frac{1}{a}}\]
\[=\frac{a}{b^2}\times \frac{a}{1}=\frac{a^2}{b^2}\]

Answer 7

since\(a\) is cosine and \(b\) is sine, this is \(\frac{\cos^2(x)}{\sin^2(x)}=\cot^2(x)\)

Answer 8

I worked the first one out and i got cot^2x. Oh my gosh I completely forgot about cos/sin. Thank you!!!

Answer 9

How would I go about finishing the next one?