SOLUTION: 2Sinx-tanx+cscx=0

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Question 258894: 2Sinx-tanx+cscx=0
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!


2%2ASin%28x%29-Tan%28x%29%2BCsc%28x%29=0

+2%2ASin%28x%29-%28Sin%28x%29%29%2F%28Cos%28x%29%29%2B1%2F%28Sin%28x%29%29=0

Multiply thru by Sin%28x%29Cos%28x%29

2%2ASin%5E2x%2ACos%28x%29-Sin%5E2x%2BCos%28x%29=0

Sin%5E2x%282Cos%28x%29-1%29%2BCos%28x%29=0

%281-Cos%5E2x%29%282Cos%28x%29-1%29%2BCos%28x%29=0

2Cos%28x%29-1-2Cos%5E3x%2BCos%5E2x%2BCos%28x%29=0

3Cos%28x%29-1-2Cos%5E3x%2BCos%5E2x=0

-2Cos%5E3x%2BCos%5E2x%2B3Cos%28x%29-1=0

2Cos%5E3x-Cos%5E2x-3Cos%28x%29%2B1=0

Trouble is that has no rational solutions,

so the only solution that is between -1 and 1 is

Cos(x)=.32103682

which gives the approximate solutions

x = 71.27436128° and 288.7256387°

as the only solutions between 0° and 360°

Edwin