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

If a=3, b=4, c=5, find the value of tan( B/2) .

if A+B=45^@ find the value of (1+tan A)(1+ tan B)

If A + B = 45^(@), "show that",(1 + tan A) (1 + tan B) = 2 , "hence find the value of " tan (22 1/2)^(@)

In triangleABC, angleA=60, b = sqrt(3)+1 and c = sqrt(3)-1 then the value of tan ((B-C)/2) is-

If a^(2) +b +2a sqrtb =7+ 4sqrt3 and c^(2) +d -2csqrtd =1 then find the value of (a + b +c +d) .

Column I, Column II sin^(-1)(4/5)+2tan^(-1)(1/3)= , p. pi/6 ; sin^(-1)(12/13)+cos^(-1)(4/5)+tan^(-1)(63/16)= , q. pi/2 . If A=tan^(-1)((xsqrt(3))/(2lambda-x))a n d B=tan^(-1)((2x-lambda)/(lambdasqrt(3))) then the value of A-B is , r. pi/4 tan^(-1)1/7+2tan^(-1)1/3= , s. pi

If I_n=int_0^(sqrt(3))(dx)/(1+x^n),(n=1,2,3. .), then find the value of ("lim")_(n to oo)I_ndot (a)0 (b) 1 (c) 2 (d) 1/2

If sin A= 1/sqrt2 " and" sinB = 1/sqrt3,"find the value of " "tan"(A+B)/2 "cot" (A-B)/2

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)))

In a right angle triangle ABC, right angle is at B ,If tan A=sqrt(3) , then find the value of (i) sin A cos C+ cos A sin C " "(ii) cos A cos C -sin A sin C