(ii)1+2ab-(a^(2)+b^(2))

Factorize each of the following expressions: a^(2)-b^(2)-a-b25x^(2)-10x+1-36y^(2)1-2ab-(a^(2)+b^(2))

Factorize each of the following expressions: x^(2)+2xy+y^(2)-a^(2)+2ab-b^(2)25x^(2)-10x+1-36y^(2)1-2ab-(a^(2)+b^(2))

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

Factorize each of the following expressions: 1-2ab-(a^(2)+b^(2))

If the length of perpendicular from origin to the line ax+by+a+b=0 is p , then show that : p^(2)-1=(2ab)/(a^(2)+b^(2))

(i ) If the length of perpendicular from origin to the line ax+by+a+b=0 is p , then show that : p^(2)-1=(2ab)/(a^(2)+b^(2)) (ii) If the length of perpendicular from point (1,1) to the line ax-by+c=0 is unity then show that : (1)/(a)-(1)/(b)+(1)/(C )=(c )/(2ab)

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))

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)

Prove that ("sin"^(-1)(2ab)/(a^(2)+b^(2))+"sin"^(-1)(2cd)/(c^(2)+d^(2))) can be expressed in the form "sin"^(-1)(2xy)/(x^(2)+y^(2)) where x and y are rational functions of a,b,c and d.

If cos alpha+ cos beta= a and sin alpha+ sin beta =b , then show that sin 2 alpha+ sin 2 beta =2 ab(1- (2)/(a^(2)+ b^(2))) .