Expert: Richard J. Raridon - 4/12/2010

Question
I could not find the path to the answers of these three problems.

1) Show:(((csc^3 X)-(cscXcot^2 X))/cscX)-sins^2 X= cos^2 X

2)Show:(cscX/(secX-tanX))-(cscX/(secX+tanX))=2secX

3)Show:(sec^2 X/(sec^2 X - 1))-1=cot^2 X

Answer
1) cancel out cscX and you have (1/sin^2X -cos^2X/sin^2X) -sin^2X = cos^2X
then (1-cos^2X)/sin^2X -sin^2X = cos^2X
sin^2X/sin^2X -sin^2X = cos^2X
1-sin^2X = cos^2X
cos^2X = cos^2X
2) [cscX(secX+tanX)-cscX(secX-tanX)]/(sec^2X-tan^2X) = 2secX
2cscXtanX/1 = 2secX
2(1/sinX)(sinX/cosX) = 2secX
2/cosX = 2secX
2secX = 2secX
3) (sec^2X/tan^2X) -1 = cot^2X
(1/sin^2X) -1 = cot^2X
csc^2X -1 = cot^2X
cot^2X = cot^2X