Prove that `l||m||n`

If l,m and n are three straight lines such that l||m and l||n then prove that m||n .

If l_(m,n)=intx^(m)cosnxdx, then prove that l_(m,n)=(x^(m)sinnx)/(n)+(mx^(m-1)cosnx)/(n^(2))-(m(m-1))/(n^(2))l_(m-2,n)

If a = x^(m + n) . Y^(l), b = x^(n + l). Y^(m) and c = x^(l + m) . Y^(n) , Prove that : a^(m-n) . b^(n - 1) . c^(l-m) = 1

If L(m,n)=int_(0)^(1)t^(m)(1+t)^(n),dt , then prove that L(m,n)=(2^(n))/(m+1)-n/(m+1)L(m+1,n-1)

If L(m,n)=int_(0)^(1)t^(m)(1+t)^(n),dt , then prove that L(m,n)=(2^(n))/(m+1)-n/(m+1)L(m+1,n-1)

If L(m,n)=int_(0)^(1)t^(m)(1+t)^(n),dt , then prove that L(m,n)=(2^(n))/(m+1)-n/(m+1)L(m+1,n-1)

If the direction cosines of a straight line are l,m and n, then prove that l^(2)+m^(2)+n^(2)=1

A B C D is a parallelogram. L\ a n d\ M are points on A B\ a n d\ D C respectively and A L=C M . Prove that L M\ a n d\ B D bisect each other.

A B C D is a parallelogram. L\ a n d\ M are points on A B\ a n d\ D C respectively and A L=C M . Prove that L M\ a n d\ B D bisect each other.

If l ,\ m,\n are three lines such that l || m\ a n d\ n_|_l , prove that n_|_mdot