SOLUTION: Prove that "1+sin^2x=csc^2x-cot^2x+sin^2x"

Question 594379: Prove that "1+sin^2x=csc^2x-cot^2x+sin^2x"
Found 2 solutions by lwsshak3, jsmallt9:
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Prove that "1+sin^2x=csc^2x-cot^2x+sin^2x"
Starting with right side:
csc^2x-cot^2x+sin^2x
=1/sin^2-cos^2/sin^2+sin^2
=1-cos^2/sin^2+sin^
=sin^2/sin^2+sin^2
=1+sin^2
verified:
right side=left side
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

There are many techniques to proving identities (equations that are true for all x's. One technique is to match terms. We already have a match (which I have highlighted in red):

We will leave the matched terms alone. Now we must find a way to show that the remaining terms on each side are equal. The unmatched terms are 1, and . If we know our properties well we know that one of the Pythagorean properties has exactly those three terms:
. If we subtract from each side we get:

So we can substitute the right side for the 1 in your equation giving us:

And we are finished.
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