SOLUTION: Can you help me solve this please? The question says, "find solutions between [0, 2PI)" The problem is sin(2theta)=sqrt(2)cos(theta) Thank You!!!!

Question 769266: Can you help me solve this please?
The question says, "find solutions between [0, 2PI)"
The problem is
sin(2theta)=sqrt(2)cos(theta)
Thank You!!!!
Found 2 solutions by lwsshak3, Alan3354:
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
find solutions between [0, 2PI)"
sin(2theta)=sqrt(2)cos(theta)
sin2x=√2 cosx
2sinxcosx=√2cosx
divide both sides by cos x
2sinx=√2
sinx=√2/2
x=π/4, 3π/4 (in Q1 and Q2 where sin>0)
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
sin(2theta)=sqrt(2)cos(theta)
---------

Use the double angle identity for sin(2t)

cos(t) = 0
t = pi/2, 3pi/2
---------------

t = pi/4, 3pi/4
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