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

If A=[cos alpha sin alpha-sin alpha cos alpha], then verify that A^(T)A=I_(2)

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,=[[sin alpha,cos alpha-cos alpha,sin alpha]], verify that A^(T)A=I_(2)

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

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

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

If {:A=[(costheta,-sintheta),(sintheta,costheta)]:},"then" A^T+A=I_2 , if

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.

{:A=[(cos^2 alpha,cosalphasinalpha),(cosalphasinalpha,sin^2alpha)]:} {:B=[(cos^2 beta,cosbetasinbeta),(cosbetasinbeta,sin^2beta)]:} are two matrices such that the product AB is the null matrix, then (alpha-beta) is