Question

If a, b, c be all +ve and p, q, r $\in$ R then evaluate the determinant
$△=$ $\left|\begin{array}{ccc}(a^p+a^{-p})& (a^p-a^{-p})& 1\\ (b^q+b^{-q})& (b^q-b^{-q})& 1\\ (c^r+c^{-r})& (c^r-c^{-r})& 1\end{array}\right|$

Answer 1

$(x^2+y^2)-(x_y{)}^2=4xy=4a^p{a}^{-p}=4$
Apply $C_1-C_2$ and take 4 common.
$\therefore △=0$.