`|((1+alpha)^2,(1+ 2alpha)^2, (1+3alpha)^2),((2+alpha)^2,(2+ 2alpha)^2, (2+3alpha)^2),((3+alpha)^2,(3+ 2alpha)^2, (3+3alpha)^2)| =-648alpha` FInd the value of `alpha`

|[(1+alpha)^(2),(1+2 alpha)^(2),(1+3 alpha)^(2)(2+alpha)^(2),(2+2 alpha)^(2),(2+3 alpha)^(2)(3+alpha)^(2),(3+2 alpha)^(2),(3+3 alpha)^(2) Find the value of alpha

Which of the following values of alpha satisfying the equation |(1+alpha)^2(1+2alpha)^2(1+3alpha)^2(2+alpha)^2(2+2alpha)^2(2+3alpha)^2(3+alpha)^2(3+2alpha)^2(3+3alpha)^2|=-648alpha? -4 b. 9 c. -9 d. 4

alpha=e^((2 pi)/(5)i)then1+alpha+alpha^(2)+alpha^(3)+alpha^(4)+2 alpha^(5)=

If f(alpha)=[[1,alpha,alpha^2],[alpha,alpha^2,1],[alpha^2,1,alpha]] then find the value of f(3^(1/3))

(1)/(tan3 alpha-tan alpha)-(1)/(cot3 alpha-cot alpha)=cot2 alpha

If A = [{:( alpha , 2),( 2,alpha ) :}] and |A^(3) | = 125 then the value of alpha is

Prove that |1alphaalpha^2alphaalpha^2 1alpha^2 1alpha|=-(1-alpha^3)^2dot

if A=[{:(alpha,2),(2, alpha):}] and |A^(3)|=125 then the value of alpha is

(tan alpha sec^(2)alpha+cot alpha cos ec^(2)alpha)-(tan alpha+cot alpha)=2cos ec2 alpha[sec^(2)alpha+cos ec^(2)alpha-3]

sin alpha-sin2 alpha+sin3 alpha=4cos(3 alpha)/(2)cos alpha sin(alpha)/(2)