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

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

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)))

Consider the following statements concerning a DeltaABC (i) The sides a,b,c and area of triangle are rational. (ii) a, "tan"(B)/(2),"tan"(C)/(2) (iii) a, sin A sin B, sin C are rational . Prove that (i) rArr(ii) rArr(iii)rArr(i)

Tangent and normal are drawn at the point P-=(16 ,16) of the parabola y^2=16 x which cut the axis of the parabola at the points Aa n dB , rerspectively. If the center of the circle through P ,A ,a n dB is C , then the angle between P C and the axis of x is (a)tan^(-1)(1/2) (b) tan^(-1)2 (c)tan^(-1)(3/4) (d) tan^(-1)(4/3)

In Delta ABC if tan(A/2) tan(B/2) + tan(B/2) tan(C/2) = 2/3 then a+c

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

In DeltaABC , if (sin A)/(c sin B) + (sin B)/(c) + (sin C)/(b) = (c)/(ab) + (b)/(ac) + (a)/(bc) , then the value of angle A is

If cos theta=a/(b+c), cos phi= b/(a+c) and cos psi=c/(a+b) where theta, phi, psi in (0, pi) and a,b,c are sides of triangle ABC then tan^2(theta/2)+tan^2(phi/2)+tan^2(psi/2)=

sum_(r=1)^nsin^(-1)((sqrt(r)-sqrt(r-1))/(sqrt(r(r+1)))) is equal to (a) tan^(-1)(sqrt(n))-pi/4 (b) tan^(-1)(sqrt(n+1))-pi/4 (c) tan^(-1)(sqrt(n)) (d) tan^(-1)(sqrt(n)+1)

In Delta ABC, prove that (a^(2) - b^(2) + c^(2)) tan B = (a^(2) + b^(2) - c^(2)) tan C.