SOLUTION: How do i solve: {{{ sin(x/2) + cos(x/2) = sqrt( 2 ) }}} Thanks!

Algebra ->  Trigonometry-basics -> SOLUTION: How do i solve: {{{ sin(x/2) + cos(x/2) = sqrt( 2 ) }}} Thanks!      Log On


   

Question 969685: How do i solve:
+sin%28x%2F2%29+%2B+cos%28x%2F2%29+=+sqrt%28+2+%29+
Thanks!
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
+sin%28x%2F2%29+%2B+cos%28x%2F2%29+=+sqrt%28+2+%29+
sqrt%28%281-cosx%29%2F2%29+%2Bsqrt%28%281%2Bcosx%29%2F2%29++=+sqrt%28+2+%29+
square both sides:
%281-cosx%29%2F2+%2B2%2Asqrt%28%281-cosx%29%281%2Bcosx%29%2F4%29%2B%281%2Bcosx%29%2F2++=+2+
%281-cosx%29%2F2+%2B2%2Asqrt%28%281-cos%5E2%28x%29%29%2F4%29%2B%281%2Bcosx%29%2F2++=+2+
%281-cosx%29%2F2+%2B2%2Asqrt%28%28sin%5E2%28x%29%29%2F4%29%2B%281%2Bcosx%29%2F2++=+2+
%281-cosx%29%2F2+%2Bsinx%2B%281%2Bcosx%29%2F2++=+2+
sinx+1=2
sinx=1
x=π/2
check:
sin(x/2)+cos)x/2)=√2/2+√2/2=√2