Show that `tan ^(-1) n+cot ^(-1)(n+1)=tan ^(-1)(n^2+n+1)`

Show that 'tan ^(-1) (m/n)-tan ^(-1) ((m-n)/(m+n))=pi/4'

sum_(r=1)^(n) tan^(-1)(2^(r-1)/(1+2^(2r-1))) is equal to a) tan^(-1)(2^n) b) tan^(-1)(2)^n-pi/4 c) tan^(-1)(2^(n+1)) d) tan^(-1)(2^(n+1))-pi/4

The value of tan^(-1)(1/2tan2A) +tan^(-1)(cotA)+tan^(-1)(cot^3A), for 0 lt A lt pi//4 is a) tan^(-1)2 b) tan^(-1)(cotA) c) 4 tan^(-1)(1) d) 2 tan^(-1)(2)

Show that x^n-1 is divisible by x-1

tan^(-1)""(m)/(n)-tan^(-1)""(m-n)/(m+n) is equal to a) tan^(-1)""(n)/(m) b) tan^(-1)""(m+n)/(m-n) c) (pi)/(4) d) tan^(-1)((1)/(2))

Prove that cos^(-1)((1-x^(2n))/(1+x^(2n)))=2 tan^(-1)x^n

If A=[[1 , 1, 1],[ 1, 1, 1],[ 1, 1 , 1]] , prove that A^n=[[3^(n-1), 3^(n-1) , 3^(n-1)],[ 3^(n-1), 3^(n-1) , 3^(n-1)],[ 3^(n-1) , 3^(n-1), 3^(n-1)]] n in N .

If a_(1), a_(2), a_(3), ………., a_(n) are in AP with common difference 5 and if a_(i)a_(j) ne -1 for i, j = 1, 2, …….., n, then tan^(-1)((5)/(1+a_(1)a_(2))) + tan^(-1)((5)/(1+a_(2)a_(3))) +……..+ tan^(-1)((5)/(1+a_(n-1)a_(n))) is equal to a) tan^(-1)((5)/(1+a(n)a_(n-1))) b) tan^(-1)((5)/(1+a(n)a_(n))) c) tan^(-1)((5n-5)/(1+a(n)a_(n+1))) d) tan^(-1)((5n-5)/(1+a_(1)a_(n)))

If "sin"(theta+phi)=n"sin"(theta-phi),n ne1 , then the value of ("tan"theta)/("tan"phi) is a) n/(n-1) b) (n+1)/(n-1) c) n/(1-n) d) (n-1)/(n+1)

If X = [{:( 1,1), ( 1,1):}]then X ^(n) , for n in N, is equal to : a) 2 ^(n -1) X b) n ^(2)X c) nX d) 2 ^(n +1) X