SOLUTION: Prove the identity csc x- cos x cot x = sin x

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Question 1027158: Prove the identity csc x- cos x cot x = sin x
Found 2 solutions by Fombitz, MathTherapy:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
csc%28x%29-cos%28x%29cot%28x%29=sin%28x%29
1%2Fsin%28x%29-cos%28x%29%2A%28cos%28x%29%2Fsin%28x%29%29=sin%28x%29
Multiply both sides by sin%28x%29,
1-cos%5E2%28x%29=sin%5E2%28x%29
sin%5E2%28x%29%2Bcos%5E2%28x%29=1
True for all values of x.

Answer by MathTherapy(10553) About Me  (Show Source):
You can put this solution on YOUR website!

Prove the identity csc x- cos x cot x = sin x
csc+%28x%29+-+cos+%28x%29+cot+%28x%29+=+highlight%28sin+%28x%29%29

The left side will be proven to be equal to the right side

1%2Fsin+%28x%29+-+cos+%28x%29+%2A+%28cos+%28x%29%2Fsin+%28x%29%29 ------- Replacing matrix%281%2C3%2C+csc+%28x%29%2C+with%2C+1%2Fsin+%28x%29%29, and matrix%281%2C3%2C+cot+%28x%29%2C+with%2C+cos+%28x%29%2Fsin+%28x%29%29  

1%2Fsin+%28x%29+-+cos%5E2+%28x%29%2Fsin+%28x%29

%281+-+cos%5E2+%28x%29%29%2Fsin+%28x%29 

sin%5E2+%28x%29%2Fsin+%28x%29 ------- Replacing matrix%281%2C3%2C+1+-+cos%5E2+%28x%29%2C+with%2C+sin%5E2+%28x%29%29

%28sin+%28x%29+%2A+sin+%28x%29%29%2Fsin+%28x%29 = %28sin+%28x%29+%2A+cross%28sin+%28x%29%29%29%2Fcross%28sin+%28x%29%29 = highlight_green%28sin+%28x%29%29

highlight_green%28sin+%28x%29%29+=+highlight%28sin+%28x%29%29 (PROVEN)