If `A=[[cosalpha, sinalpha],[-sinalpha, cosalpha]]`, prove by mathematicasl induction that, `A^n=[[cosnalpha, sin nalpha],[-sin nalpha,cos nalpha]]` for every natural number n

If A=[[cosalpha, -sin alpha] , [sin alpha, cos alpha]] then A+A'=I then alpha=

If A=[(cosalpha,sinalpha),(-sinalpha,cosalpha)] prove that A.A^(T)=1 Hence find A^(-1)

If A= [[cosalpha,sinalpha],[-sinalpha,cosalpha]] then show that A^2=[[cos2alpha,sin2alpha],[-sin2alpha,cos2alpha]]

If A_alpha=[[cosalpha ,sinalpha],[-sinalpha,cosalpha]] , then prove that A_alphaA_beta=A_(alpha+beta) for every positive integer n .

If f(alpha)=[[cosalpha,-sinalpha,0],[sinalpha,cosalpha,0],[ 0, 0, 1]],t h e n prove that [F(alpha)]^(-1)=F(-alpha)dot

If A=[cosalpha+sinalpha,sqrt(2)sinalpha; -sqrt(2)sinalpha,cosalpha-sinalpha] , prove that A^n=[cosn\ alpha+sinn\ alpha, sqrt(2)sinn\ alpha; -sqrt(2)sinn\ alpha, cosn\ alpha-sinn\ alpha] for all n in Ndot

sinalpha+sinbeta=a ,cosalpha+cosbeta=b=>sin(alpha+beta)

Prove that (sinalpha)/(1+cosalpha)+(1+cosalpha)/(sin alpha)=2"cosec "alpha .

Prove by using principle of induction that: cos alpha+cos 2alpha+…+cos n alpha = sin. (nalpha)/2 cosec alpha/2 cos. ((n+1)alpha)/2

If sinalpha+sinbeta=a ,cosalpha+cosbeta=b=>sin(alpha+beta) =