Question

evaluate determinant ​

Answer 1

Answer:

$(tanA -1)^2$

Step-by-step explanation:

$det.\left[\begin{array}{ccc}0&1&secA\\tan A&-secA&tan A\\1&0&1\end{array}\right]\\= 0[(-secA *1) -(tan A*0)] - tanA[(1*1)-(secA*0)] - 1[(1*tanA) - (-secA*secA)]\\=0 - tanA - tan A+ sec^2A\\=1+tan^2A - 2tanA\\=(tanA- 1)^2$