Su Prove that the product of two THAILS cose cost-sino cos.o cospsing Jcose sinesineaanacos | sinsina Odd check of The product of is a zero matrix if the difference of 6 and 0 FIN

Prove that the product of matrices [cos^2thetacosthetasinthetacosthetasinthetasin^2theta] and [cos^2varphicosvarphisinvarphicosvarphisinvarphisin^2varphi] is the null matrix, when theta and varphi differ by an odd multiple of pi/2 .

Prove that the product of matrices [cos^(2)theta cos theta sin theta cos theta sin theta s in^(2)theta] and [cos^(2)varphi cos varphi sin varphi cos varphi sin varphi s in^(2)varphi] is the null matrix,when theta and varphi differ by an odd multiple of (pi)/(2) .

Flind the product of two matrices A =[[cos^(2) theta , cos theta sin theta],[cos theta sin theta ,sin^(2)theta]] B= [[cos^(2) phi,cos phi sin phi],[cos phisin phi,sin^(2)phi]] Show that, AB is the zero matrix if theta and phi differ by an odd multipl of pi/2 .

Flind the product of two matrices A =[[cos^(2) theta , cos theta sin theta],[cos theta sin theta ,sin^(2)theta]] B= [[cos^(2) phi,cos phi sin phi],[cos phisin phi,sin^(2)phi]] Show that, AB is the zero matrix if theta and phi differ by an odd multipl of pi/2 .

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.

Prove that in any arithmetic progression , whose common difference is not equal to zero, the product of two terms equidistant from the extreme terms is the greater as it will move to the middle term .

23, Prove that the product of the lengths of the perpendiculars drawn from thepoints (a?-B,0) and (-Va -B,0) to the line cos 0 sin 6 =lis B.

The beta - decay process , discovered around 1900 , is basically the decay of a neutron n . In the laboratory , a proton p and an electron e^(bar) are observed as the decay product of neutron. Therefore considering the decay of neutron as a two- body decay process, it was predicted theoretically that the kinetic energy of the electron should be a constant . But experimentally , it was observed that the electron kinetic energy has continuous spectrum Considering a three- body decay process , i.e. n rarr p + e^(bar) + bar nu _(e) , around 1930 , Pauli explained the observed electron energy spectrum. Assuming the anti-neutrino (bar nu_(e)) to be massaless and possessing negligible energy , and the neutrino to be at rest , momentum and energy conservation principle are applied. From this calculation , the maximum kinetic energy of the electron is 0.8 xx 10^(6) eV The kinetic energy carried by the proton is only the recoil energy. If the - neutrono had a mass of 3 eV// c^(2) (where c is the speed of light ) insend of zero mass , what should be the range of the kinectic energy K. of the electron ?

Find the cubic polynomial with the sum of its zeroes, sum of the products of its zeroes taken two at a time and product of its zeroes as 0, -7 and - 6 respectively.

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