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

If sinx+cosecx=2 , then, for all n in N , the value of: sin^nx+cosec^nx= (a) 2 (b) 2^n (c) 2^(n-1) (d) 2^(n-2)

lim_(x->0) (sin(nx)((a-n) nx-tan x))/ x2., when n is a non-zero positive integer, then a is equal to

Consider the following statements I.n(sin^(2)(67(1)/(2^(@)))-sin^(2)(22(1)/(2^(@))))>1 for all positive integers n>=2. II If x is any positive real number,then nx>1 for all positive integers n>=2. Which of the above statement(s) is/are correct?

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

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 .

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

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

Using mathematical induction prove that (d)/(dx)(x^(n))=nx^(n-1) for all positive integers n.

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) .