sec (a-x) , sec a , sec (a+x) are in AP.... Proove, cos a=Root2 (cos (x/2))
2/cos(a) = 1/cos(a+x) + 1/cos(a-x)
= [cos(a-x) +cos(a+x)]/cos(a+x)cos(a-x)
= 2cos(a)cos(x)/[(1/2)(cos(2a) + cos(2x)
cos(2a) + cos(2x) = 2cos^2(a)*cos(x)
2cos^2(a) - 1 +2cos^x - 1 = 2cos^2(a)*cos(x)
cos^2(a) +cos^2(x) -1 = cos^2*cos(x)
cos^2(x) -1 = cos^2a*cos(x) - cos^2(a)
[cos(x) + 1][cos(x) - 1] = cos^2(a)[cos(x) - 1]
cos(x) + 1 = cos^2(a)
2cos^2(x/2) = cos^2(a)
cos(a) = sqrt(2)*cos(x/2)