If `cosx+secx=-2` then for a positive integer n, `cos^nx+sin^nx` is

int nx^(n-1) cosx^n dx

lim_(x->0) (sin(nx)((a-n)nx – tanx))/x^2= 0 , when n is a non-zero positive integer, then a is equal to

Solve the equation sin mx + sin nx = 0

If n is a positive integer, prove that: int_0^(2pi) (cos(n-1)x-cosnx)/(1-cosx)dx=2pi , hence or otherwise, show that int_0^(2pi) (sin((nx)/2)/sin(x/2))^2dx=2npi .

Let n be a positive integer if 1le1gt K len such that (sin^(2)nx)/(sin^(2)x)=a_(@)+sum_(1ge i lt klen) a_(1,k) cos 2 (k-1) for all real number x with x not an integer multiple of pi , then the value of a_(1,k) is

If sinx+cosecx=2," then "sin^nx+cosec^nx is equal to

If and n are positive integers, then lim_(x->0)((cosx)^(1/ m)-(cosx)^(1/ n))/(x^2) equal to :

Let n be a positive integer such that sin (pi/(2n))+cos (pi/(2n))= sqrt(n)/2 then (A) n=6 (B) n=1,2,3,….8 (C) n=5 (D) none of these

If [x] denotes the greatest integer less than or equal to x and n in N , then f(X)= nx+n-[nx+n]+tan""(pix)/(2) , is

For a positive integer n, let I _(n) int _(-pi)^(pi) ((pi)/(2) -|x|) cos nx dx Find the value of [I _(1) + I _(3) +I_(4)] where [.] denotes greatest integer function.