q89
sinA+cosA=

7/2
since sinA=2tan(A/2)/1+tansquare(A/2)
also cosA=1-tansquare(A/2)/1+tansquare(A/2)
therefore
2tan(A/2)+1-tansquare(A/2)/(1+tansquare(A/2)=

7/2
(
7+2)tansquare(A/2)-4tan(A/2)+(

7-2)=0
solving we get tan(A/2)=2+- 1/(

7+2)
since A<pi/6
therefore tan(A/2)=2-1/

7+2
tan(A/2)=

7-2/3
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