First slide

Trigonometric equations

Question

$The equation \cos^{8} x + b \cos^{4} x + 1 = 0 will have solution if b \in$

Moderate

A

$(- \infty, 2]$
B

$(- \infty,- 2]$
C

$[2, \infty)$
D

$(0, 1)$

Solution

Given equation can be written as
$\begin{array}{l} b = - (\cos^{4} x + \frac{1}{\cos^{4} x}) \\ \Rightarrow b \in (- \infty, - 2] \end{array}$

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