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

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

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

If sin(pi costheta) = cos(pi sintheta) , show that, +- cos(theta +-pi/4) = (4n+-1)/(2sqrt(2)) , where n= any integer.

(i) If sin(pi/2costheta) = cos(pi/2 sin theta) , show that, +- cos(theta + pi/4) =(4n+1)/sqrt(2) where n= any integer. (ii) If tan(pi cos theta) = cot(pi sin theta) , prove that, cos(theta - pi/4) = (2n+1)/(2sqrt(2)), n=0, -1,1,-2,2 ,............

Find the minimum value of n for which tan^(-1)((n)/(pi))>(pi)/(4),n in N

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

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

If 4cos x sin x*2sin x = 3sin x, then x = (i) n pi+(-1)^(n) (pi)/(10) (ii) n pi-(-1)^(n) ( pi)/(10) (iii) 2n pi+-(pi)/(10) (iv) n pi+(pi)/(10)

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