If `A=[costhetasintheta-sinthetacostheta]`, then prove that `A^n=[cosnthetasinntheta-sinnthetacosntheta], n in N`.

Find the inverse of the matrix [costhetasintheta-sinthetacostheta] .

If A = [[cos^2theta, costhetasintheta],[costhetasintheta, sin^2theta]] B= [[cos^2phi, cosphisinphi], [cosphisinphi, sin^2phi]] and theta - phi = (2n+1)(pi)/2 Find AB.

Prove that 2^(n)>n,n in N

Prove that P(n,n)=2.P(n,n-2)

Prove that: n!(n+2)=n!+(n+1)!

Prove that [n+1/2]^(n)>(n!)

If A=[1101], prove that A^(n)=[1n01] for all positive integers n.

Prove that n!(n+2)=n!+(n+1)!

Prove that quad 2^(n)>n for all positive integers n.

Using mathematical induction prove that : (d)/(dx)(x^(n))=nx^(n-1)f or backslash all n in N