First slide

Theory of expressions

Question

Minimum value of $4 x^{2} - 4 x |\sin θ| - \cos^{2} θ$ is

Moderate

A

$- 2$
B

$- 1$
C

$- \frac{1}{2}$
D

0

Solution

$W e h a v e 4 x^{2} - 4 x |\sin θ| - \cos^{2} θ$
$\begin{array}{l} = 4 x^{2} - 4 x |\sin θ| - (1 - \sin^{2} θ) \\ = - 1 + {(2 x - |\sin θ|)}^{2} \\ ∴ M i n i m u m V a l u e = - 1 \end{array}$

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