a  and  b  are real and ax+(sinb)y+(cosb)z=0;  x+(cosb)y+(sinb)z=0;  −x+(sinb)y−(cosb)z=0  The set of all values of ‘a’ for which the system of linear equations has a non-trivial solutions is

For non-trivial solution, Δ=|a      sinb       cosb1       cosb      sinb−1    sinb    −cosb|=0  ⇒a[−cos2b−sin2b]−sinb[−cosb+sinb]+cosb[sinb+cosb]=0  ⇒−a+sin2b+cos2b=0  ⇒a=cos2b+sin2b=2cos(2b−π4)   Since, −1≤cos(2b−π4)≤1  ⇒−2≤2cos(2b−π4)≤2 ⇒−2≤a≤2  ⇒a∈[−2,2]