SOLUTION: If x is a positive acute angle and cosx = 1/9, what is the value of cos 1/2x?

SOLUTION: If x is a positive acute angle and cosx = 1/9, what is the value of cos 1/2x?

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Question 445781: If x is a positive acute angle and cosx = 1/9, what is the value of cos 1/2x?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
If x is a positive acute angle and cosx = 1/9, what is the value of cos 1/2x?
..
Use half-angle formula for cosine with positive sqrt because x/2 is positive
cos(x/2)=sqrt((1+cosx)/2)
=sqrt((1+1/9)/2)
=sqrt((10/9)/2)
=sqrt(5/9)
cos(x/2)=√5/3 (ans)
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