" 29."1+2ab-(a^(2)+b^(2))

Factorise : 1 + 2 ab - (a ^(2) + b ^(2))

If a and b are real and i=sqrt(-1) then sin[i ln((a+ib)/(a-ib))] is equal to 1) (2ab)/(a^(2)-b^(2)) 2) (-2ab)/(a^(2)-b^(2)) 3) (2ab)/(a^(2)+b^(2)) 4) (-2ab)/(a^(2)+b^(2))

If (x+1)/(x-1)=(a)/(b) and (1-y)/(1+y)=(b)/(a), then the value of (x-y)/(1+xy) is (2ab)/(a^(2)-b^(2)) (b) (a^(2)-b^(2))/(2ab) (c) (a^(2)+b^(2))/(2ab) (d) (a^(2)-b^(2)backslash)/(ab)

The factors of 8a^(3)+b^(3)-6ab+1 are (a) (2a+b-1)(4a^(2)+b^(2)+1-3ab-2a) (b) (2a-b+1)(4a^(2)+b^(2)-4ab+1-2a+b)(2a+b+1)(4a^(2)+b^(2)+1-2ab-b-2a) (d) (2a-1+b)(4a^(2)+1-4a-b-2ab)

The value of the determinant |{:(1+ a^(2) - b^(2),2 ab , - 2b),(2ab, 1 - a^(2) + b^(2), 2a),(2b , -2a , 1-a^(2) - b^(2)):}| is equal to

If [ sqrt (a ^(2) + b^(2) + ab)] + [ sqrt (a^(2) + b^(2) - ab)] = 1 then what is the value of (1 - a^(2)) (1 - b^(2)) ?

Answer any three questions Using properties of determinants, prove the following abs{:(1+a^2 - b^2,2ab,-2b),(2ab,1-a^(2) +b^(2) ,2a),(2b,-2a,1-a^2 -b^2):}=(1+a^2 +b^2)^3.

Prove that |(2ab,a^(2),b^(2)),(a^(2),b^(2),2ab),(b^(2),2ab,a^(2))|=-(a^(3)+b^(3))^(2) .

If a+b+ c =9 and a^(2) + b^(2) + c^(2) = 29 , find ab + bc + ca .

Show that |{:(1+a^(2)-b^(2),,2ab,,-2b),(2ab,,1-a^(2)+b^(2),,2a),(2b,,-2a,,1-a^(2)-b^(2)):}| = (1+a^(2) +b^(2))^(3)