Evaluate `sin{ n pi+(-1)^(n) (pi)/(4)`, where n is an integer.

Evaluate tan{(-1)^n pi/4} where n is an integer

Prove that : tan^(-1) (e^(itheta)) = (n pi)/2 + pi/4 +i/2 ln" tan(pi/4 + theta /2) ,where n is an integer.

Evaluate: tan{2t a n-1 1/5+pi/4}

If A= [(3 , -4), (1 , -1) ] , then prove that A^n=[(1+2n , -4n), (n , 1-2n) ] , where n is any positive integer.

evaluate lim_(n->oo)((e^n)/pi)^(1/ n)

evaluate lim_(n->oo)((e^n)/pi)^(1/ n)

Find lim_(xrarr(2n+1)pi^(+)) sin([sinx](pi)/6) , where [.] is a greatest integer function and "n" epsilonI .

The equatin 2x = (2n +1)pi (1 - cos x) , (where n is a positive integer)

The minimum value of n for which tan^(-1)'n/pi gt (pi)/(4), n in N , is valid is 5.

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.