Let n be a positive integer such that `sin(pi/2n) + cos(pi/2n) = sqrt(n)/2`

Let n be a positive integer such that sin((pi)/(2^(n)))+cos((pi)/(2^(n)))=(sqrt(n))/(2), then

The number of positive integers which satisfy sin((pi)/(4n))+cos((pi)/(4n))=sqrt((n)/(2)) is -

Determine a positive integer n such that (pi)/(2)x^(n)sin xdx=(3)/(4)(pi^(2)-8)

The least positive integer n such that [{:(cos""(pi)/(4), sin""(pi)/(4)) ,(- sin ""(pi)/(4) , cos ""(pi)/(4)):}]^(n) is an identity matrix of order 2 is

The least positive integer n such that ((2i)^n)/((1-i)^(n-2)),i=sqrt(-1) , is a positive integer,is ______

If n is a positive integer and (1+i)^(2n)=k cos(n pi/2) , then the value of k is

If n is be a positive integer,then (1+i)^(n)+(1-i)^(n)=2^(k)cos((n pi)/(4)), where k is equal to

Prove that (a)(1+i)^(n)+(1-i)^(n)=2^((n+2)/(2))*cos((n pi)/(4)) where n is a positive integer. (b) (1+i sqrt(3))^(n)+(1-i sqrt(3)^(n)=2^(n+1)cos((n pi)/(3)), where n is a positive integer

If U_(n)=int_(0)^( pi)(1-cos nx)/(1-cos x)dx, where n is positive integer or zero,then show that U_(n+2)+U_(n)=2U_(n+1). Hence,deduce that int_(0)^((pi)/(2))(sin^(2)n theta)/(sin^(2)theta)=(1)/(2)n pi

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) .