Question 832147: Find all solutions in the interval [0, 2pi)
Sec^2x付anx= 2tanx
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! sec^2(x) * tan(x) = 2*tan(x)
sec^2(x) * tan(x) - 2*tan(x) = 0
tan(x)( sec^2(x) - 2 ) = 0
tan(x) = 0 or sec^2(x) - 2 = 0
tan(x) = 0 or sec^2(x) = 2
tan(x) = 0 or sec(x) = sqrt(2) or sec(x) = -sqrt(2)
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Solve each equation for x
tan(x) = 0
x = arctan(0)
x = 0 or x = pi
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sec(x) = sqrt(2)
x = arcsec(sqrt(2))
x = pi/4 or x = 7pi/4
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sec(x) = -sqrt(2)
x = arcsec(-sqrt(2))
x = 3pi/4 or x = 5pi/4
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The 6 solutions in the interval [0, 2pi) are...
x = 0,
x = pi,
x = pi/4,
x = 7pi/4,
x = 3pi/4,
x = 5pi/4
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