First slide

Trigonometric equations

Question

If the equation $\cot^{4} x - 2 \cos e c^{2} x + a^{2} = 0$ has at least one solution then, sum of all possible integral values of ‘a’ is equal to

Moderate

A

4
B

3
C

2
D

0

Solution

$W e h a v e \cot^{4} x - 2 \cos e c^{2} x + a^{2} = 0$
$\Rightarrow \cot^{4} x - 2 (1 + \cot^{2} x) + a^{2} = 0$
$\Rightarrow \cot^{4} x - 2 \cot^{2} x + a^{2} - 2 = 0$
$\Rightarrow {(\cot^{2} x - 1)}^{2} = 3 - a^{2}$
To have at least one solution $3 - a^{2} \geq 0$
$\Rightarrow a^{2} - 3 \leq 0$
$a \in [- \sqrt{3}, \sqrt{3}]$
$\Rightarrow a = - 1, 0, 1$
$∴$ sum of all values of ‘a’ = 0

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