If 2a+b = pi/2, prove that cos a = +- root [(1+sin b)/2]?

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2007-11-06 04:14:03 · 2 answers · asked by cutiepie1334 1 in Science & Mathematics ➔ Mathematics

2a=pi/2-b
cos2a=cos(pi/2-b)
2(cosa)^2-1=sinb
cosa)^2=(1+sinb)/2
cosa=+-sqrt[(1+sinb)/2]

2007-11-06 04:41:51 · answer #1 · answered by katsaounisvagelis 5 · 0⤊ 0⤋

2a+b = pi/2
2a = (pi/2 -b) Now use 1/2 angle formula in next step:
cos 2a/2 =cos a = +/- sqrt(1-cos(pi/2-b)/2)
= +/- sqrt((1+sinb)/2)

2007-11-06 12:50:02 · answer #2 · answered by ironduke8159 7 · 0⤊ 0⤋