If `A=[costhetaisinthetaisinthetacostheta],` then prove by principal of mathematical induction that

If A=[[costheta,isintheta],[isintheta,costheta]], then prove by principal of mathematical induction that A^n=[[cosntheta, i sinn theta],[isin n theta, cos n theta]] for all nin NN.

Second principal of mathematical induction

First principle of mathematical induction

Prove by the principle of mathematical induction that n<2^(n) for alln in N

Using principle of mathematical induction prove that sqrt(n) =2

Prove by using principle of mathematical induction :2^(n)<3^(n),n in N

Introduction and Steps of Mathematical Induction

What are the Algorithm(steps involving in mathematical induction)

Prove the following by the principle of mathematical induction: 1+2+2^(7)=2^(n+1)-1 for all n in N