SOLUTION: Solve each equation for all values of theta. the problem is sin(theta/2) plus cosine(theta/2)= sqrt(2)

Algebra ->  Trigonometry-basics -> SOLUTION: Solve each equation for all values of theta. the problem is sin(theta/2) plus cosine(theta/2)= sqrt(2)      Log On


   

Question 32773: Solve each equation for all values of theta. the problem is sin(theta/2)
plus cosine(theta/2)= sqrt(2)
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
sin(x/2) + cos(x/2)=sqrt(2)
sqrt[(1-cosx)/2] + sqrt[(1+cosx)/2] = sqrt(2)
Square both sides to get:
1/2 + 1/2 +[sqrt(1-cos^2(x))/2]=2
sqrt[(1-cos^2(x))/2]=1
Square both sides again to get:
(1-cos^2(x))/2=1
1-cos^2(x)=1
cos^2(x)=0
cos(x)=0
x=90 or 270 degrees.
Cheers,
Stan H.