Question 736672: i need help solving for tan theta + cot theta is equal to sec theta over sin theta
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! tan theta + cot theta is equal to sec theta over sin theta
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tan + cot = sec/sin
tan + 1/tan = 1/(sin*cos)
(tan^2 + 1)/tan = 1/(sin*cos)
sec^2/tan = 1/(sin*cos)
sec^2*cos/sin = 1/(sin*cos)
Multiply by sin
sec^2*cos = 1/sin
sec = 1/sin
1/cos = 1/sin
cos = sin
cos^2 = sin^2 = 1 - cos^2
2cos^2 = 1
cos^2 = 1/2
cos = sqrt(2)/2
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theta = pi/4, 3pi/4
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Those are the principal values.
You can add or subtract 2pi*n to/from them, n = 1, 2, 3...
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