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

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

(-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.

Solve (x-1)^(n)=x^(n), where n is a positive integer.

Find the value of (-1)^(n)+(-1)^(2n)+(-1)^(2n_1)+(-1)^(4n+2) , where n is any positive and integer.

Find the value of n, where n is an integer and 2^(n-5)xx6^(2n-4)=1/(12^(4)xx2)

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

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