1)

The set of real values of α for which the system of linear equations

 x+(sinα)y+(cosα)z=0

x+(cosα)y+(sinα)z=0

x+(sinα)y(cosα)z=0

has a non-trivial solution is 


A) nπ2+(1)nπ4+π8 (n is an integer)

B) nπ2+(1)nπ8 (n is an integer)

C) nπ2+(1)nπ8π8 (n is an integer)

D) nπ2+(1)nπ4π8 (n is an integer)

Answer:

Option C

Explanation:

 x+sinαy+cosαz=0,x+cosαy+sinαz=0

  x+sinαycosαz=0

 Non-trivial sol, so  

[1sinαcosα1cosαsinα1sinαcosα]=0

      |1(sin2αcos2α)sinα(cosα+sinα)+cosα(sinα+cosα)|=0

 1sinα(cosα+sinα]+cosα[sinα+cosα]=0

1+sinαcosαsin2α+sinαcosα+cos2α=0

    1+sin2α+cos2α=0

sin2α+cos2α=1

         12sinα+12cosα=12

     sin(2α+π4)=sinπ4

    2α+π4=nπ+(1)nπ4 

               2α=nπ+(1)nπ4π4

    α= nπ2+(1)nπ8π8