Question #359ad

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Answer 1 · 2017-12-06T15:34:26

#arctan(cosx/(1-sinx))=pi/4+x/2#

#cosx/(1-sinx)#

=#[(cos(x/2))^2-(sin(x/2))^2]/(cos(x/2)-sin(x/2))^2#

=#[(cos(x/2)-sin(x/2))*(cos(x/2)+sin(x/2))]/(cos(x/2)-sin(x/2))^2#

=#(cos(x/2)+sin(x/2))/(cos(x/2)-sin(x/2))#

=#(1+tan(x/2))/(1-tan(x/2))#

=#tan(pi/4+x/2)#

Thus,

#arctan(cosx/(1-sinx))=pi/4+x/2#