SOLUTION: if 0&#8804;&#920;<360°, solve sec^2 (2&#920;) +2sec(2&#920;) = 0

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Question 979124: if 0≤Θ<360°, solve sec^2 (2Θ) +2sec(2Θ) = 0
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If 0%5Eo%3C=theta%3C360%5Eo<-->0%5Eo%3C=2theta%3C720%5Eo , solve sec%5E2%282theta%29%2B2sec%282theta%29=0
Factoring:
sec%5E2%282theta%29%2B2sec%282theta%29=0--->sec%282theta%29%28sec%282theta%29%2B2%29=0--->system%28sec%282theta%29=0%2C%22or%22%2Csec%282theta%29%2B2=0%29
sec%282theta%29=0 does not happen for any value of theta ,
because the function secant never takes any value between -1 and 1.
sec%282theta%29%2B2=0-->sec%282theta%29=-2-->1%2Fcos%282theta%29=-2-->cos%282theta%29=-1%2F2-->2theta=k%2A360%5Eo+%2B-+120%5Eo for some integer k .
With the restriction 0%5Eo%3C=2theta%3C720%5Eo ,
the values that make 2theta=k%2A360%5Eo+%2B-+120%5Eo for some integer k are
2theta=120%5Eo<--->highlight%28theta=60%5Eo%29 , or
2theta=240%5Eo<--->highlight%28theta=120%5Eo%29 , or
2theta=480%5Eo<--->highlight%28theta=240%5Eo%29 , or
2theta=600%5Eo<--->highlight%28theta=300%5Eo%29 .