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lim(x-(pi)/(4))(1-sin2x)/(1+cos4x)...

lim_(x-(pi)/(4))(1-sin2x)/(1+cos4x)

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Evaluate lim_(xto(pi)/(4)) (1-sin2x)/(1+cos4x).

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lim_(xto(pi)) (1-sin(x/2))/(cos(x/2)(cos(x/4)-sin(x/4)))

Putting z=x-(pi)/(4), show that lim_(x rarr(pi)/(4))(1-tan x)/(1-sqrt(2)sin x)=2