Match the following Column I to Column II

Explanation

(A) `|x-1|+|x-3|=3/2`
Case `1:x ge3`
`x-1+x-3=3//2`
`implies2x=3//2+4=11//2`
`impliesx=11//4lt3`
No solution
Case`2:1 lexlt3`
`(x-1)-(x-3)=3//2`
`impliesx-1-x=33//2`
`2 ne3//2` No solution
Case `3: x lt 1`
`-(x-1)-(x-3)=3//2`
`implies-2x+4=3//2`
`implies-2x=3//2-4`
`implies -2x=-5//2 `
`n=4//4 gt1` No solution
(B) Given `(cos40^(@))/(sin40^(@))-(cos50^(@))/(sin50^(@))=k(cos80^(@))/(sin80^(@))implies(sin10^(@))/(sin40^(@)sin50^(@))=(k.cos80^(@))/(sin80^(@))`
`implies(2sin80^(@))/(2 sin40^(@)sin50^(@))=kimplies(2cos10^(@))/(cos90^(@)+cos10^(@))=k`
So, `k=3`
(C ) If `A+B+C=pi//2, then`
`sumtanA tanB=i`
(D) `If A+B+C=pi`
then `sum cot""(A)/(2)=picot""A/2`
So, `(cot13^(@)+cot26^(@)+cot51^(@))/(cot13^(@)cot26^(@)cot51^(@))=1Ans."]"`