For the system of linear equations to have non trivial solution, |
1
sin‌α
cos‌α
1
cos‌α
sin‌α
−1
sin‌α
−cos‌α
|=0 (1(−sin2α−cos2α)−sin‌α(−cos‌α+sin‌α)+cos‌α(sin‌α+cos‌α))=0 −1−sin‌α(−cos‌α+sin‌α)+cos‌α(sin‌α+cos‌α)=0 sin‌2‌α+cos‌2‌α=1 Further simplify the above,