`|[sinA, cosA, sin(A+theta)] , [sinB, cosB, sin(B+theta)] , [sinC, cosC, sin(C+theta)]|=`

Prove that, |[sin A, cosA, sin(A+theta)],[sinB, cosB, sin(B+theta)],[sinC, cosc, sin(C+theta)]| =0

Using properties of determinant. Prove that | [sinA, cosA, sinA + cosB], [sinB, cosA, sinB + cosB], [sinC, cosA, sinC + cosB] | = 0

Using properties of determinant. Prove that |[sinA,cosA,sinA+cosB],[sinB,cosA,sinB+cosB],[sinC,cosA,sinC+cosB]|=0

If |[cos(A+B), -sin(A+B), cos2B], [sinA, cosA, sinB], [-cosA, sinA, cosB]|=0 , then B=

|[sin^2A, sinA, cos^2A] , [sin^2B, sinB, cos^2B] , [sin^2C, sinC, cos^2C]|=-(sinA-sinB)(sinB-sinC)(sinC-sinA)

The determinant |{:(sinA,cosA,sinA+cosB),(sinB,cosA,sin+cosB),(sinC,cosA,sinC+cosB):}| is equal to zero

sin(A-B)=sinA cos B-cosA sinB

If 16sin^(5)theta=sin a theta+b sin c theta+d sin theta then a+b+c+d=