SOLUTION: Hey, I have this question proving trigononmetric identities. I was given, {{{(sinx/1-cosx)+((1-cosx)/sinx) =2cscx}}} I have already tried some things, I might be off track, but th

Algebra ->  Trigonometry-basics -> SOLUTION: Hey, I have this question proving trigononmetric identities. I was given, {{{(sinx/1-cosx)+((1-cosx)/sinx) =2cscx}}} I have already tried some things, I might be off track, but th      Log On


   



Question 170808: Hey, I have this question proving trigononmetric identities. I was given, %28sinx%2F1-cosx%29%2B%28%281-cosx%29%2Fsinx%29+=2cscx I have already tried some things, I might be off track, but this is what I have done. I am working on the left side of the equal sign. I multiplied (sin/sin) to the left side of the plus sign, and (1-cosx/1-cosx) to the right side of the plus sign. I then combined the two sides of the plus sign to get %28%28sinx%5E2%29%2B%282-cosx%5E2%29%2F%281-cosxsinx%29%29. Then I am not sure what to do. The properties we were given were the reciprocal properties, quotient properties, and the pythagorean properties. Please help?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Hey, I have this question proving trigononmetric identities. I was given, %28sinx%2F1-cosx%29%2B%28%281-cosx%29%2Fsinx%29+=2cscx I have already tried some things, I might be off track, but this is what I have done. I am working on the left side of the equal sign. I multiplied (sin/sin) to the left side of the plus sign, and (1-cosx/1-cosx) to the right side of the plus sign. I then combined the two sides of the plus sign to get %28%28sinx%5E2%29%2B%282-cosx%5E2%29%2F%281-cosxsinx%29%29. Then I am not sure what to do. The properties we were given were the reciprocal properties, quotient properties, and the pythagorean properties. Please help?
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Is the 1st term sinx/1 ?? What's the point of that?
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%28sinx%2F%281-cosx%29%29%2B%28%281-cosx%29%2Fsinx%29+=2cscx
Multiply by (1-cos(x))
sin%28x%29+%2B+%281-cos%28x%29%29%5E2%2Fsin%28x%29+=+2csc%28x%29%2A%281-cos%28x%29%29
Multiply by sin(x)
sin^2(x) + (1-cos(x))^2 = 2(1-cos(x))}}}
sin^2(x) + 1 -2cos(x) + cos^2(x) = 2 - 2cos(x)}}}
Since sin^2 + cos^2 = 1,
2 -2cos(x) does = 2 - 2cos(x)
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I log onto the site, and there are 400 problems to look at, each from someone looking for help. If you can't bother to get the problem right, you chances of help drop from 1 out of 400 to a lot less.