If `A=[sinalphacosalpha-cosalphasinalpha]` , verify that `A^T\ A=I_2` .

If A=[[sinalpha,cosalpha],[-cosalpha,sinalpha]] , verify that A^T A=I_2

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

If (i) A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] , then verify that AprimeA = I .(ii) A=[[sinalpha,cosalpha],[-cosalpha,sinalpha]] , then verify that AprimeA = I .

If A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] , then verify that A^T\ A=I_2 .

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

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

The sides of the triangle are sin alpha , cos alpha and sqrt(1+sinalphacosalpha) for some 0 lt alpha lt (pi)/2 . Then the greatest angle of the triangle is

Without expanding, show that the value of each of the determinants is zero: |sinalphacosalpha"cos"(alpha+delta)sinbetacosbeta"cos"(beta+delta)singammacosgamma"cos"(gamma+delta)|

If z= 6+8i , verify that |z|= |bar(z)|