MCQ
$[(a \times b) \times (b \times c)\,(b \times c) \times (c \times a)\,(c \times a) \times (a \times b)] = \,$
- A${[a\,\,b\,\,c]^2}$
- B${[a\,\,b\,\,c]^3}$
- ✓${[a\,\,b\,\,c]^4}$
- DNone of these
$(b \times c) \times (c \times a) = ((b \times c)\,.\,a)c - ((b \times c)\,.\,c)a = [\,b\,c\,a]\,c$
$(c \times a) \times (a \times b) = ((c \times a)\,.\,b)a - ((c \times a)\,.\,a)b = [c\,a\,b]\,a$
$\therefore \,\,\,[(a \times b) \times (b \times c)(b \times c) \times (c \times a)(c \times a) \times (a \times b)]$
$ = [[a\,b\,c]\,a\,[a\,b\,c]\,b\,[a\,b\,c]\,c]$$ = {[a\,b\,c]^3}[a\,b\,c] = {[a\,b\,c]^4}.$
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$\mathrm{f}(\mathrm{x})=\log _{\sqrt{5}}(3+\cos \left(\frac{3 \pi}{4}+\mathrm{x}\right)+\cos \left(\frac{\pi}{4}+\mathrm{x}\right)+\cos \left(\frac{\pi}{4}-\mathrm{x}\right)$
$-\cos \left(\frac{3 \pi}{4}-\mathrm{x}\right))$ is :