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 neither alpha nor beta is a multiple of pi/2 and the product AB of matrices A=[(cos^2alpha, cosalpha sin alpha),(cosalpha sinalpha, sin^2alpha)] and B=[(cos^2beta, cosbeta sinbeta),(cosbetasinbeta, sin^2beta)] is a null matrix then alpha- beta is (A) 0 (B) an odd mutiple of pi/2 (C) a multiple of pi (D) none of these

{: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

If A=[(cos^(2)alpha, cos alpha sin alpha),(cos alpha sin alpha, sin^(2)alpha)] and B=[(cos^(2)betas,cos beta sin beta),(cos beta sin beta, sin^(2) beta)] are two matrices such that the product AB is null matrix, then alpha-beta is

det[[cos alpha cos beta,cos alpha sin beta,-sin alpha-sin beta,cos beta,0sin alpha cos beta,sin alpha sin beta,cos alpha]]

Evaluate ,,,|cos alpha cos beta,cos alpha sin beta,-sin alpha-sin beta,cos beta,0sin alpha,cos beta,sin alpha sin beta,cos alpha]|

Evaluate: quad =|cos alpha cos beta cos alpha sin beta-sin alpha-sin beta cos beta0sin alpha cos beta sin alpha sin beta cos alpha|

Find the value of, cos alpha cos beta, cos alpha sin beta, -no alpha-sin beta, cos beta, 0 sin alpha cos beta, sin alpha sin beta, cos alpha] |

If cos alpha+cos beta=0=sin alpha+sin beta then cos2 alpha+cos2 beta=

(sin^(2)alpha-sin^(2)beta)/(sin alpha cos alpha-sin beta cos beta)=tan(alpha+beta)