If `(a+(1)/(a))^(2)= 3`, then `a^(3)+(1)/(a^(3))` equals

If (a+(1)/(a))^(2)=9 , then a^(3)+(1)/(a^(3)) equals

If x lt -(1)/sqrt(3) , then tan^(-1)(3x-x^(3))/(1-3x^(2)) equals

If -(1)/sqrt(3) lt x lt (1)/sqrt(3), then tan^(-1) (3x-x^(3))/(1-3x^(2)) equals

If x gt (1)/sqrt(3) then tan^(-1) (3x-x^(3))/(1-3x^(2)) equals

The sum of the infinite series (1)/(2) ((1)/(3) + (1)/(4)) - (1)/(4)((1)/(3^(2)) + (1)/(4^(2))) + (1)/(6) ((1)/(3^(3)) + (1)/(4^(3))) - ...is equal to

If sin theta=(1)/(2) (a+(1)/(a)) and sin 3 theta=(k)/(2)(a^(3)+(1)/(a^(3))) , then k+6 is equal to :

(1+2i)/(1+3i) is equal to

3(1)/(5)+1(2)/(3) is equal to