SOLUTION: For the problem: Find all solutions to 2cos^2(theta) -1=0 I need to find all solutions I would rearrange to get cos2(theta)=1/2 why doesn't it go from cos2(theta) to 1-sin^

Algebra ->  Finance -> SOLUTION: For the problem: Find all solutions to 2cos^2(theta) -1=0 I need to find all solutions I would rearrange to get cos2(theta)=1/2 why doesn't it go from cos2(theta) to 1-sin^      Log On


   

Question 964566: For the problem:
Find all solutions to
2cos^2(theta) -1=0
I need to find all solutions
I would rearrange to get cos2(theta)=1/2
why doesn't it go from cos2(theta) to 1-sin^2(theta)=1/2 since of the identity for cos(2(theta))?
I don't understand how it only becomes cos2(theta)=1/2 to become pi/6? what about the other identity? and what does 2(theta) mean exactly? why is the answer pi/6?
Please help
Thank you
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You should get the same answer either way since it is an identity.
cos%5E2%28theta%29=1%2F2
cos%28theta%29=+0+%2B-+sqrt%281%2F2%29
theta=%281%2F4%29pi and theta=%283%2F4%29pi and
theta=%285%2F4%29pi and theta=%287%2F4%29pi
.
.
.
1-sin%5E2%28theta%29=1%2F2
-sin%5E2%28theta%29=-1%2F2
sin%5E2%28theta%29=1%2F2
sin%28theta%29=+0+%2B-+sqrt%281%2F2%29
theta=%281%2F4%29pi and theta=%283%2F4%29pi and
theta=%285%2F4%29pi and theta=%287%2F4%29pi
.
.
.
Not sure where pi%2F6 comes into it?