First slide

Trigonometric Identities

Question

$\cos e c^{2} α = \frac{4 x y}{{(x + y)}^{2}} [(x, y) \neq (0, 0)]$ is

Moderate

A

Possible for x = y
B

Impossible for x = y
C

Possible for x = - y
D

Not possible

Solution

$∵ \cos e c α \in (- \infty, - 1] \cup [1, \infty)$
$\Rightarrow \cos e c^{2} α \geq 1 \Rightarrow \frac{4 x y}{{(x + y)}^{2}} \geq 1 \Rightarrow {(x + y)}^{2} - 4 x y \leq 0 \Rightarrow {(x - y)}^{2} \leq 0 \Rightarrow x = y$

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