Q) If cos(x-y), cos(x),cos(x+y) are in H.P.,then cos(x).sec(y/2) is equal to?

A)
Solving the whole thing using AM(arithmetic mean) concept we finally get
cos^2x.cosy = cos^2y + cos^2x - 1
cos^2 x = (1-cos^2y) / (1-cosy)
cos^2 x = 1 + cos y
cos^2 x = 2cos^2(y/2)
cos^2 x. sec^2 (y/2) = 2
cosx.sec(y/2) = +- rt (2)

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