If `u_(n)=2Cos^(n) theta then show that u_(1)u_(n)-u_(n-1)= u_(n+1)

If u_(n) = cos^(n) theta + sin^(n) theta then 2u_(6)-3u_(4)=

Show that If I _(n) =int cos ^(n) x dx, then show that I_(n) =1/n cos ^(n-1) x sin x + (n-1)/(n ) I_(n-2).

If sum_(i=1)^(n)sin theta_(i)=n then cos theta_(1) + cos theta_(2) + ...+cos theta_(n)=

If n is an integer and z=cis theta,(theta ne (2n+1)pi/2), then show that (z^(2n)-1)/(z^(2n)+1)=i tan n theta) .

If n is integer and z = cis theta, ( theta ne ( 2n + 1) pi//2) , then show that (z ^(2n) -1)/(z^(2n) +1) = i tan n theta .

If U_(n) = sin n theta.sec^(n)theta, V_(n)=cosnthetasec^(n)theta for n=0,1,2,……. Then V_(n)-V_(n-1) + U_(n-1) tan theta = ?

Let A=((1,0,0),(2,1,0),(3,2,1)) . If u_(1) and u_(2) are column matrices such that Au_(1)=((1),(0),(0)) and Au_(2)=((0),(1),(0)) then u_(1)+u_(2) is equal to

Bohr proposed his atomic model based on Planck.s quantum theory and derived following relations for one electron system in C.G.S. units : For H -atom : r_(n) = n^(2) xx r_(1), E_(n) = E_(1) xx Z^(2), u_(n) = (u_(1))/(n), u_(1) = 2.19 xx 10^(8) cm//sec., E_(1) = -13.6eV For 1 electron system, other than H r_(n) = (n^(2) xx r_(1H))/(Z), E_(N) = (E_(1H) xx Z^(2))/(n^(2)), u_(n) = (u_(1H) xx Z)/(n) . Later on de Broglie proposed the dual nature of electron and put forward his wave concept. The wave length of electron in an orbit was given lambda = h/mu The potential energy of electron in 3^(rd) Bohr orbit of H-atom is :

Bohr proposed his atomic model based on Planck.s quantum theory and derived following relations for one electron system in C.G.S. units : For H -atom : r_(n) = n^(2) xx r_(1), E_(n) = E_(1) xx Z^(2), u_(n) = (u_(1))/(n), u_(1) = 2.19 xx 10^(8) cm//sec., E_(1) = -13.6eV For 1 electron system, other than H r_(n) = (n^(2) xx r_(1H))/(Z), E_(N) = (E_(1H) xx Z^(2))/(n^(2)), u_(n) = (u_(1H) xx Z)/(n) . Later on de Broglie proposed the dual nature of electron and put forward his wave concept. The wave length of electron in an orbit was given lambda = h/mu The circumference (in m) of 3^(rd) Bohr orbit in H-atom is :

If n is an integer then show that (1 + cos theta + i sin theta)^(n) + (1 + cos theta - i sin theta )^(n) = 2^(n+1) cos ^(n) ( theta//2) cos ((n theta)/2) .