Is the relationship `2sinx=a+(1/a)` true, where a is any positive integer.

Write any five positive integers.

Write the expansion of (a+b)^n , where n is any positive integer.

If ((1+i)/(1-i))^x=1 then (A) x=2n+1 , where n is any positive ineger (B) x=4n , where n is any positive integer (C) x=2n where n is any positive integer (D) x=4n+1 where n is any positive integer

If A is any square matrix, prove that (A^n)' = (A')^n , where n is any positive integer.

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

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

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

Consider the integral I_(m) = int_(0)^(pi) (sin2mx)/(sinx ) dx , where m is a positive integer. What is I_(1) equal to ?

If A,=[[3,-41,1]], then prove that A^(n),=[[1+2n,-4n][2n], where n is any positive integer.