Question

If the equation ${\cot }^{4}x-2co{\sec }^{2}x+a^2=0$ 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

The correct option is D $0$

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