Solve the equation sin6x + cos6x = 1/4.
Suat Namli
Solve the equation sin6x + cos6x = 1/4.
Solution
Put a = sin2x, b = cos2x. Then a and b are non-negative with sum 1, so we may put a = 1/2 + h, b = 1/2 - h. Then a3 + b3 = 1/4 + 3h2 ≥ 1/4
with equality iff h = 0.
Hence x is a solution of the equation given iff
sin2x = cos2x = 1/2 or x is an odd multiple of π/4.
Thanks to
; 05-11-2013 02:09 AM
: 1 (0 1 )
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