Question

answer the question what is maximum value of​

Answer 1

Step-by-step explanation:

Let the given determinant be

$y = \cos(x) ( \cos(x) - 1) - ( - \sin(x) ). \sin(x)$

$\implies \: y = \cos^{2} (x) - \cos(x) + \sin^{2} (x)$

$\implies \: y = \cos^{2} (x) + \sin^{2} (x) - \cos(x) +$

$\implies \: y =1- \cos(x)$

We know,

$- 1 \leqslant \cos(x) \leqslant 1$

$\implies \: 1 \geqslant - \cos(x) \geqslant - 1$

$\implies \: 1 + 1 \geqslant 1 - \cos(x) \geqslant - 1 + 1$

$\implies \: 2 \geqslant 1 - \cos(x) \geqslant 0$

$\implies \: 0\leqslant 1 - \cos(x) \leqslant 2$

So, minimum value of y is 0