If `a,b,c` be positive real numbers and the value of `theta=tan^(- 1)sqrt((a(a+b+c))/(b c))+tan^(- 1)sqrt((b(a+b+c))/(c a)) + tan^-1sqrt((c(a+b+a))/((ab))` then `tan theta` is equal to

If a,b,c are positive real numbers and 2a+b+3c=1 , then the maximum value of a^(4)b^(2)c^(2) is equal to

If a, b,c are three positive real numbers , then find minimum value of (a^(2)+1)/(b+c)+(b^(2)+1)/(c+a)+(c^(2)+1)/(a+b)

In a DeltaABC, if C is a right angle, then tan^(-1)((a)/(b+c))+tan^(-1)((b)/(c+a))=

If a ,b , a n dc are distinct positive real numbers such that a+b+c=1, then prove tha ((1+a)(1+b)(1+c))/((1-a)(1-b)(1-c))> 8.

Prove that (1)/(a) + (1)/(b) + (1)/(c ) ge (1)/(sqrt((bc))) + (1)/(sqrt((ca))) + (1)/(sqrt((ab))) , where a,b,c gt 0

If sqrt(3)+i=(a+i b)(c+i d) , then find the value of tan^(-1)(b//a)+tan^(-1)(d//c)

The value of (lim)_(xvecoo)(tan^(-1)x))) is equal to (a)-1 (b) pi/2 (c) -1/(sqrt(2)) (d) 1/(sqrt(2))

Tangents are drawn to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1,(a > b), and the circle x^2+y^2=a^2 at the points where a common ordinate cuts them (on the same side of the x-axis). Then the greatest acute angle between these tangents is given by (A) tan^(-1)((a-b)/(2sqrt(a b))) (B) tan^(-1)((a+b)/(2sqrt(a b))) (C) tan^(-1)((2a b)/(sqrt(a-b))) (D) tan^(-1)((2a b)/(sqrt(a+b)))

The value of tan^(-1)((xcostheta)/(1-xsintheta))-cot^(-1)((costheta)/(x-sintheta))i s 2theta (b) theta (c) theta/2 (d) independent of theta

IF ( sec A - tan A) ( sec B - tan B) ( sec C- tan C ) =(sec A + tan A ) ( sec B + tan B ) ( secC + tan C ) then each is equal to