Question #04d3d

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Answer 1 · 2018-01-21T18:27:10

#x=pi/2#

#sinx+cot(x/2)=2#

#(2cot(x/2))/[(cot(x/2))^2+1]+cot(x/2)=2#

Set #u=cot(x/2)#, this integral became

#(2u)/(u^2+1)+u=2#

#(2u)/(u^2+1)+u-2=0#

#(u-2)*(u^2+1)+2u=0#

#u^3-2u^2+u-2+2u=0#

#u^3-2u^2+3u-2=0#

#(u-1)*(u^2-u+2)=0#

From second multiplier, no real solution. From first one, #u=1#

Thus,

#cot(x/2)=1#

#x/2=pi/4#, so #x=pi/2#