If `A=[cosalphasinalpha-sinalphacosalpha]` is such that `A^T=A^(-1),fin dalpha`

If A_alpha=[cosalphasinalpha-sinalphacosalpha] , then prove that (A_alpha)^n=[cos n\ alphasinn\ alpha-sinn\ alpha cos n\ alpha] for every positive integer n .

If A_alpha=[cosalphasinalpha-sinalphacosalpha],t h e nA_alphaA_beta= (a)A_(alpha+beta) (b) A_(alphabeta) (c) A_(alpha-beta) (D) None of these

If (i) A=[cosalphasinalpha-sinalphacosalpha] , then verify that AprimeA" "=" "I . (ii) A=[sinalphacosalpha-cosalphasinalpha] , then verify that AprimeA" "=" "I .

If A=(cosalpha-sinalpha0sinalphacosalpha0 0 0 1), find a d jdotA and verify that A(a d jdotA)=(a d jdotA)A=|A|I_3dot

Evaluate : (cos^3alpha + sin^3alpha)/(1-sinalphacosalpha)

If A=[(cos^2alpha,cosalphasinalpha),(cosalphasinalpha,sin^2alpha)] and B=[(cos^2beta,cosbetasinbeta),(cosbetasinbeta,sin^2beta)] . Show that AB=[(cosalphacosbetacos(alpha-beta),sinbetacosalphacos(alpha-beta)),(cosbetasinalphacos(alpha-beta),sinbetasinalphacos(alpha-beta))]

If 1+sin^2alpha=3sinalphacosalpha , then the values of cotalpha are

Prove that the product of the matrices [[cos^2alpha, cosalphasinalpha],[cosalphasinalpha,sin^2alpha]] and [[cos^2beta,cosbetasinbeta],[cosbetasinbeta,sin^beta]] is the null matrix when alpha and beta differ by an odd multiple of pi/ 2.

If alphaandbeta are not the multiple of (pi)/(2)and [{:(cos^(2)alpha,cosalphasinalpha),(cosalphasinalpha,sin^(2)alpha):}]xx[{:(cos^(2)beta,sinbetacosbeta),(sinbetacosbeta,sin^(2)beta):}]=[{:(0,0),(0,0):}] then alpha-beta is ......

If p sin^(3)alpha+qcos^(3)alpha=sinalphacosalpha and p sinalpha - q cos alpha=0, then prove that : p^(2)+q^(2)=1