Question #aee32

1 Answer
Dec 4, 2017

#-Sin^3x/(1+cosx) + cos^3x/(1+sinx) #

#=-(Sin^3x(1-cosx))/((1+cosx)(1-cosx)) + (cos^3x(1-sinx))/((1+sinx)(1-sinx)) #

#=-(Sin^3x(1-cosx))/(1-cos^2x) + (cos^3x(1-sinx))/(1-sin^2x) #

#=-(Sin^3x(1-cosx))/(sin^2x) + (cos^3x(1-sinx))/(cos^2x) #
#=-Sinx(1-cosx))+ cosx(1-sinx) #

#=cosx-sinx#
#=sqrt2(1/sqrt2cosx-1/sqrt2sinx)#

#=sqrt2(cos(pi/4)cosx-sin(pi/4)sinx)#

#= sqrt 2(cos (pi/4 +x)#