Without expanding show that: $=|\cos e{c}^2\theta {\cot }^2\theta 1{\cot }^2\theta \cos e{c}^2\theta -142402|=0$

Let △=|(A x,x^2, 1),(B y, y^2, 1),(C z, z^2, 1)| and△1=|(A,B, C),( x, ...

If Delta1=|[a, b, c],[ x, y, z],[ p, q, r]| and Delta2=|[q,-b, y],[-p,...

Find the value of the determinant =|2 3 4 5 6 8 6x9x 12 x|dot

Without expanding evaluate the determinant |[41,1,5],[79,7,9],[29,5,3]...

Show that matrix |(1,a,b+c),(1,b,c+a),(1,c, a+b)|=0

Without expanding evaluate the determinant |(x^2+x^(-1))^2(a^2-a^(-1))...

If 1=|(1, 1, 1),(x^2,y^2,z^2),(x, y ,z)|a n d2=|(1 ,1, 1),(y z, z x,x ...

Without expanding show that |[b^2c^2,b c, b+c],[c^2a^2,c a ,c+a ],[a^2...

Without expanding evaluate the determinant |[sinalpha,cosalpha,sin(alp...

If A+B+C=pi, then the value of |[sin(A+B+C),sin(A+C),cosC],[-sinB,0...

If Ar=|[1,r,2^r],[2,n,n^2],[n,(n(n+1))/2, 2^(n+1)]|, the value of sum(...

If the determinant |[a,b,2aalpha+3b],[b,c,2balpha+3c],[2aalpha+3b,2bal...

If a , b , c are distinct, then the value of x satisfying |(0,x^2-a, x...

Using the factor theorem it is found that a+b , b+c and c+a are thr...

Let |(x^2+3x,x-1,x+3),(x+1,-2x x-4),(x-3,x+4 ,3x)|=a x^4+b x^3+c x^2+e...

If Dk=|[1,n,n],[2k,n^2+n+2,n^2+n],[2k-1,n^2,n^2+n+2]| and sum(k=1)^...

If Delta1=|(1, 1, 1),(a, b, c),( a^2,b^2,c^2)|,Delta2=|(1,bc, a),(1,ca...

The value of the determinant |(a^2,a,1),(cosn x,cos(n+1)x,cos(n+2)x),(...

Evaluate: (i) |(5 ,4),(-2, 3)| (ii) |(sintheta,costheta),(-costheta,s...