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Question Number 74130 by mathocean1 last updated on 19/Nov/19
hello] help me to solve it in ]−Π;Π]×]−Π;Π] please   { ((x−y=(Π/6))),((cosx−(√3)cosy=−(1/2))) :}
hello]helpmetosolveitin]Π;Π]×]Π;Π]please{xy=Π6cosx3cosy=12
Answered by Tanmay chaudhury last updated on 19/Nov/19
cos((π/6)+y)−(√3) cosy=((−1)/2)  ((√3)/2)cosy−(1/2)siny−(√3) cosy=((−1)/2)  ((−1)/2)siny−((√3)/2)cosy=((−1)/2)  (1/2)siny+((√3)/2)cosy=(1/2)  sin((π/3)+y)=sin(π/6)  (π/3)+y=(π/6)→y=−(π/6)  so x=y+(π/6)→x=0  sin((π/3)+y)=sin(π/6)=sin(π−(π/6))  (π/3)+y=((5π)/6)→y=((5π)/6)−((2π)/6)=(π/2)  x=(π/6)+y→x=(π/6)+((3π)/6)=((4π)/6)
cos(π6+y)3cosy=1232cosy12siny3cosy=1212siny32cosy=1212siny+32cosy=12sin(π3+y)=sinπ6π3+y=π6y=π6sox=y+π6x=0sin(π3+y)=sinπ6=sin(ππ6)π3+y=5π6y=5π62π6=π2x=π6+yx=π6+3π6=4π6

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