SOLUTION: Please help me solve this problem. Solve the equation on the interval 0<= theta

SOLUTION: Please help me solve this problem. Solve the equation on the interval 0<= theta < 2 pi. tan^2 theta = (3/2) sec theta

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): You can put this solution on YOUR website!
Please help me solve this problem.
Solve the equation on the interval 0<= theta < 2 pi.
tan^2 theta = (3/2) sec theta
**
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

RELATED QUESTIONS
please help me to solve this equation : 3 ( SEC THETA - TAN THETA)= 2 COS THETA (answered by Alan3354)

solve the equation on the interval 0 < or equal to theta < 2pi. tan^2 theta = 3/2 sec... (answered by lwsshak3)

Please solve the equation: sec theta- tan theta=0 for... (answered by solver91311)

solve the equation on the interval 0 < or equal to theta < 2 pi. tan theta = cot... (answered by lwsshak3)

solve the equation cos theta - tan theta * cos theta = 0 for 0< theta < 2... (answered by stanbon,DrBeeee)

Please help me, I am so lost. The problem is: solve the equation on the interval 0 is... (answered by htmentor)

please help me solve this trig question: 2cos2 theta+ cos theta= 1 on the interval 0_<... (answered by Fombitz)

Solve the equation 4sin^2(theta) + 2 cos(theta) = 3 for 0 < theta < 2... (answered by Theo)

Please help me solve for sin(theta) 1. cot(theta)=-1/5, (theta) is in quadrant IV 2.... (answered by stanbon)