Question

If the equation $\cot ^4 x-2 \operatorname{cosec}^2 x+a^2=0$ has atleast one solution then, sum of all possible integral values of ' $a$ ' is equal to

• A. 4
• B. 3
• C. 2
• D. 0

Answer 1

Answer: (D)

$\cot ^4 x-2\left(1+\cot ^2 x\right)+a^2=0 $
$\Rightarrow \cot ^4 x-2 \cot ^2 x+a^2-2=0$
$\Rightarrow \left(\cot ^2 x-1\right)^2=3-a^2$
to have atleast one solution
$3-a^2 \geq 0 $
$\Rightarrow a^2-3 \leq 0 $
$a \in[-\sqrt{3}, \sqrt{3}]$
integral values $-1,0,1$
$\therefore \text { sum }=0 $