Let m be a positive integer and `Deltar`=`|[2r-1,.^mC_r,1],[m^2-1,2^m,m+1],[sin^2(m^2),sin^2m,sin(m^2)]|`. Then the value of `sum_(r=0)^m Deltar`

Let m be a positive integer and Delta r=det[[m^(2)-1,*^(m)C_(r),1m^(2)-1,2^(m),m+1sin^(2)(m^(2)),sin^(2)m,sin(m^(2))]] of sum_(r=0)^(m)Delta r

If m is a positive integer and D_r=|(2r-1,\ ^m C_r,1),(m^2-1, 2^m ,m+1),(sin^2(m^2),sin^2(m),sin^2(m+1))| . Prove that sum_(r=0)^m D_r=0 .

Let t be a positive integer and |((2t-1),m^2-1,cos^2(m)),(mC_t,2^m,cos^2(m)),(1,m+1,cos(m^2))| then the value of sum_(t=0)^m Delta_t is equal to

The value of sum_(r=0)^(3m)(-1)^(r).6mC_(2r) is

The value of sum_(r=1)^(3m)(-3)^(r-1).6mC_(2r-1) is

Let T_(r) denote the rth term of a G.P.for r=1,2,3,... If for some positive integers m and n, we have T_(m)=1/n^(2) and T_(n)=1/m^(2) ,then find the value of T_(m+n/2)

2m-(1)/(2m)=2 , m!=0, in m^(2)+(1)/(16m^(2)) =?

Let z=cos theta+i sin theta then the value of sum_(m=1)^(30)Im(z^(2m-1)) at theta=2^(@) is.

(m+2)sin theta+(2m-1)cos theta=2m+1 then tan theta is