SOLUTION: Please help me solve this problem.
Solve the equation on the interval 0<= theta < 2 pi.
tan^2 theta = (3/2) sec theta
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Solve the equation on the interval 0<= theta < 2 pi.
tan^2 theta = (3/2) sec theta
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Question 585705: Please help me solve this problem.
Solve the equation on the interval 0<= theta < 2 pi.
tan^2 theta = (3/2) sec theta Answer by lwsshak3(11628) (Show Source):
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Solve the equation on the interval 0<= theta < 2 pi.
tan^2 theta = (3/2) sec theta
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use x for theta.
tan^x=(3/2)secx
Identity: tan^2=sec^2-1
sec^2x-1=(3/2)secx
sec^2x-(3/2)secx-1=0
2sec^2x-3secx-2=0
(2secx+1)(secx-2)=0
2secx+1=0
secx=-1/2 (reject, not in domain)
..
secx-2=0
secx=2=1/cosx
cosx=1/2
x=π/3 ans 5π/3 in quadrants I and IV where sec and cos>0
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