SOLUTION: Find all solutions in the interval [0, 2pi) Sec^2x�tanx= 2tanx

Question 832147: Find all solutions in the interval [0, 2pi)
Sec^2x�tanx= 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)

-----------------------------------

Solve each equation for x

tan(x) = 0

x = arctan(0)

x = 0 or x = pi

----------------

sec(x) = sqrt(2)

x = arcsec(sqrt(2))

x = pi/4 or x = 7pi/4

----------------

sec(x) = -sqrt(2)

x = arcsec(-sqrt(2))

x = 3pi/4 or x = 5pi/4

=======================================================

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

RELATED QUESTIONS
find all solutions in the interval (0, 2pi) tanxcos^2x-... (answered by Alan3354)

Find all solutions on the interval (0,2pi) Sec^2x - 2tanx... (answered by lwsshak3)

Find all solutions of the equation in the interval [0, 2pi)... (answered by lwsshak3)

Find all solutions in the interval [0, 2pi].... (answered by lwsshak3)

find all solutions: 3sin^2x+2sinx-1=0; in the interval... (answered by ikleyn)

Find all solutions of the equation in the interval [0, 2pi).... (answered by Alan3354)

Find all solutions of each equation in the interval [0, 2pi)... (answered by lwsshak3)

Find all solutions in the interval o and 2pi 1.) Cos^2x+ sinx +1= 0 (answered by lwsshak3)

Find all solutions in the interval [0,2pi)... (answered by MathLover1)