`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)`

sum_(r =1)^(n) sin^(-1) ((sqrtr - sqrt(r -1))/(sqrtr(r + 1))) is equal to

Show that "sin"^(-1)(sqrt(3))/2+"tan"^(-1)1/(sqrt(3))=(2pi)/3

tan^(-1)sqrt(3)-cot^(-1)(-sqrt(3)) is equal to (A) pi (B) -pi/2 (C) 0 (D) 2sqrt(3)

sum_(n=1)^oo sin^-1( (sqrt(n)-(sqrt(n-1)))/(sqrt((n)(n+1)) )= (A) pi/4 (B) pi/2 (C) - pi/3 (D) pi/3

Evaluate: tan^(- 1)(-1/(sqrt(3)))+tan^(- 1)(-sqrt(3))+tan^(- 1)(sin(-pi/2))

If sin^(-1)((sqrt(x))/2)+sin^(-1)(sqrt(1-x/4))+tan^(-1)y=(2pi)/3 , then

int_0^(pi//2)1/(2+cos\ x)dx equals a. 1/3tan^(-1)(1/(sqrt(3))) b. 2/(sqrt(3))tan^(-1)(1/(sqrt(3))) c. sqrt(3)tan^(-1)(sqrt(3)) d. 2sqrt(3)tan^(-1)sqrt(3)

The value of lim_(xrarr1)(sqrtpi-sqrt(4tan^(-1)x))/(sqrt(1-x)) is equal to

If y=tan^(-1){(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))},"f i n d"(dy)/(dx)

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)))