MCQ
જો [${{\left( {{\tan }^{-1}}x \right)}^{2}}+{{\left( {{\cot }^{-1}}x \right)}^{2}}=\frac{5{{\pi }^{2}}}{8},$ હોય તો $x=.........$
- ✓$-1$
- B$0$
- C$1$
- D$2$
$(tan^{-1}x)^2+(cot^{-1}x)^2=\frac{5\pi^2}{8}$
$\Rightarrow(tan^{-1}x+cot^{-1}x)^2-2tan^{-1}xcot^{-1}x=\frac{5\pi^2}{8}$
$\Rightarrow2(tan^{-1}x)^2-\pi tan^{-1}x\frac{-3\pi^2}{8}=0$
$\Rightarrow(tan^{-1}x)^2-\frac{\pi}{2}tan^{-1}x\frac{-3\pi^2}{16}=0$
$\Rightarrow tan^{-1}x=\frac{-\pi}{4}$
$\Rightarrow x=-1$
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$2 x+y-z=5$
$2 x-5 y+\lambda z=\mu$
$x+2 y-5 z=7$
ને અસંખ્ય ઉકેલો હોય,તો
$(\lambda+\mu)^2+(\lambda-\mu)^2=........$