First slide

Trigonometric Identities

Question

If for real values of $x,$ $\cos θ = x + \frac{1}{x}$ then

Easy

A

$θ$ is an acute angle
B

$θ$ is an obtuse angle
C

$θ$ is right angle
D

no value of $θ$ is possible

Solution

$x + \frac{1}{x} \geq 2 f o r x > 0$ $o r x + \frac{1}{x} \leq - 2 i f x < 0$
$\Rightarrow \cos θ \geq 2 o r \cos θ \leq - 2 T h i s i s n o t p o s s i b l e \sin c e - 1 \leq \cos θ \leq 1 \Rightarrow n o v a l u e o f θ i s p o s s i b l e$

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