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

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

Evaluate sin{ n pi+(-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}

(-i)^(4n+3) , where n Is a positive integer.

If 2 tan^(-1)(costheta) = tan^(-1)(2 cosec theta) , then show that theta = (pi)/(4) , when n is an y integer.

Find out the sum of the coefficients in the expansion of the binomial (5p - 4q)^n , where n is a +ive integer.

Using permutation or otherwise, prove that (n^2)!/(n!)^n is an integer, where n is a positive integer. (JEE-2004]

If two consecutive terms in the expansion of (x+a)^n are equal to where n is a positive integer then ((n+1)a)/(x+a) is

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