SOLUTION: Solve equation, csc^2x = cotx + 1, on the interval 0 < or equal x < 2pi

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Question 1202700: Solve equation, csc^2x = cotx + 1, on the interval 0 < or equal x < 2pi
Found 2 solutions by Edwin McCravy, math_tutor2020:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
 

 

Now use your calculator to find the inverse cotangent

Using the + sign
x=0.9830696068 answer in the first quadrant.
x=pi%2B0.9830696068=4.12466226 answer in the third quadrant.

Using the - sign
x=2pi-0.5535743589=5.729610948 answer in the fourth quadrant.
x=pi-0.5535743589=2.58891895 answer in the second quadrant.

Edwin

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

csc%5E2%28x%29+=+cot%28x%29+%2B+1

1%2Bcot%5E2%28x%29+=+cot%28x%29+%2B+1 Use a trig identity

cot%5E2%28x%29+=+cot%28x%29 Subtract 1 from both sides. The "1"s cancel.

cot%5E2%28x%29+-+cot%28x%29+=+0 Subtract cot(x) from both sides

cot%28x%29%28cot%28x%29+-+1%29+=+0 Factor

cot%28x%29=0 or cot%28x%29+-+1+=+0 Set each piece equal to zero

cot%28x%29=0 or cot%28x%29+=+1

tan%28x%29+=+0 or tan%28x%29+=+1 Use another trig identity.

I'll let the student finish up.