Prove that : `tan^(-1)( (a^3 -b^3)/(1+a^3 b^3)) + tan^(-1)( (b^3 - c^3)/(1+b^3 c^3)) + tan^(-1)( (c^3 - a^3)/(1+c^3 a^3)) = 0`

Prove that : tan^(-1)( (2a-b)/(bsqrt(3))) +tan^(-1)((2b-a)/(asqrt(3))) = pi/3

Prove that (a^8+b^8+c^8)/(a^3b^3c^3)>1/a+1/b+1/c

Prove that (a+b+c)^3 - a^3-b^3-c^3 = 3(a+b)(b+c)(c+a).

int ((tan^(-1) x )^(3))/( 1+x^(2)) dx is equal to a) 3 ( tan^(-1) x )^(2) +C b) (1)/(4) ( tan^(-1)x)^(4) +C c) ( tan^(-1) x)^(4) + C d) none of these

Prove that (a+b+c)^(3)-a^(3)-b^(3)-c^(3)=3(a+b)(b+c)(c+a) .

If the points ((a^3)/((a-1))),(((a^2-3))/((a-1))),((b^3)/(b-1)),((b^2-3)/((b-1))) , ((c^3)/(c-1)) and (((c^2-3))/((c-1))), where a , b , c are different from 1, lie on the l x+m y+n=0 , then (a) a+b+c=-m/l (b) a b+b c+c a=n/l (c) a b c=((m+n))/l (d) a b c-(b c+c a+a b)+3(a+b+c)=0

A normal to parabola, whose inclination is 30^(@) , cuts it again at an angle of (a) tan^(-1)((sqrt(3))/(2)) (b) tan^(-1)((2)/(sqrt(3))) (c) tan^(-1)(2sqrt(3)) (d) tan^(-1)((1)/(2sqrt(3)))

2tan^(-1)(-2) is equal to (a) -cos t^(-1)((-3)/5) (b) -pi+cos^(-1)3/5 (c) -pi/2+tan^(-1)(-3/4) (d) -picot^(-1)(-3/4)

If the points (a^3/(a-1),(a^2-3)/(a-1)) , (b^3/(b-1),(b^2-3)/(b-1)) , (c^3/(c-1),(c^2-3)/(c-1)) are collinear for 3 distinct values a,b,c and a!=1, b!=1, c!=1 , then find the value of abc-(ab+bc+ca)+3(a+b+c) .

If theta= tan^(-1) (2tan^2 theta) - tan^(-1) (1/3 tan theta) . Then tan theta is a) -2 b) -1 c) 2/3 d) 2