First slide

Trigonometric equations

Question

If the inequality $\sin^{2} x + acos x + a^{2} > 1 + \cos x$ holds for any $x \in R$ then the largest negative integral value of a is

Moderate

A

-4
B

-3
C

-2
D

-1

Solution

$\sin^{2} x + acos x + a^{2} > 1 + \cos x$
Putting X = 0, we have
$\begin{array}{ll} a + a^{2} > 2 \\ or a^{2} + a - 2 > 0 \\ or (a + 2) (a - 1) > 0 \\ or a < - 2 or a > 1 \end{array}$
Therefore, the largest negative integral value of a is -3.

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