`sum_(i=1)^(2n) sin^(-1)(x_i)=npi` then the value of `sum_(i=1)^n cos^(-1)x_i+sum_(i=1)^n tan^(-1)x_i=` (A) `(npi)/4` (B) `(2/3)npi` (C) `(5/4)npi` (D) `2npi`

If a_n=sin((npi)/6) then the value of sum a_n^2

If sum_(i=1)^(n) cos theta_(i)=n , then the value of sum_(i=1)^(n) sin theta_(i) .

If sum_(i=1)^10 sin^-1 x_i = 5pi then sum_(i=1)^10 x_i^2 = (A) 0 (B) 5 (C) 10 (D) none of these

Find the value of cos {npi +(-1) ^(n) (pi)/(3)}

If sum_(i=1)^(4)(sin^(-1)x_(i)+cos^(-1)y_(i))=6pi , then \int\limitsum_(i=1)^(4)x(i)^sum(i=1)^(4)y(i) xln(1+x^(2))(e^(x^(2))/(1+e^(2x)))dx is euqal to

If n= 10, sum_(i=1)^(10) x_(i) = 60 and sum_(i=1)^(10) x_(i)^(2) = 1000 then find s.d.

If sum_(i=1)^(7) i^(2)x_(i) = 1 and sum_(i=1)^(7)(i+1)^(2) x_(i) = 12 and sum_(i=1)^(7)(i+2)^(2)x_(i) = 123 then find the value of sum_(i=1)^(7)(i+3)^(2)x_(i)"____"

General solution of the equatin 1+sin^4 2x=cos^2 6x is (A) (npi)/3 (B) (npi)/2 (C) npi (D) none of these

If sum_(i=1)^n(x_i+1)^2=9n and sum_(i=1)^n(x_i-1)^2=5n , then standard deviation of these 'n' observations (x_1) is: (1) 2sqrt(3) (2) sqrt(3) (3) sqrt(5) (4) 3sqrt(2)

The number of real solution of the equation sin^(-1) (sum_(i=1)^(oo) x^(i +1) -x sum_(i=1)^(oo) ((x)/(2))^(i)) = (pi)/(2) - cos^(-1) (sum_(i=1)^(oo) (-(x)/(2))^(i) - sum_(i=1)^(oo) (-x)^(i)) lying in the interval (-(1)/(2), (1)/(2)) is ______. (Here, the inverse trigonometric function sin^(-1) x and cos^(-1) x assume values in [-(pi)/(2), (pi)/(2)] and [0, pi] respectively)