First slide

Trigonometric equations

Question

If $3 \sec^{4} x + 6 \tan^{4} x = 2$ , then solution set is

Moderate

A

$ϕ$
B

$n π$
C

$\frac{n π}{2}$
D

$2 n π$

Solution

$3 \sec^{4} x + 6 \tan^{4} x = 2$
$\Rightarrow 3 \sec^{4} x + 6 \tan^{4} x = 2 {(\sec^{2} x - \tan^{2} x)}^{2} (∵ \sec^{2} x - \tan^{2} x = 1)$
$\Rightarrow \sec^{4} x + 4 \tan^{4} x + 4 \sec^{2} x \tan^{2} x = 0$
$\Rightarrow {(\sec^{2} x + 2 \tan^{2} x)}^{2} = 0$
$\Rightarrow 1 + 2 \sin^{2} x = 0$
$\Rightarrow$ The given equation has no solution

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