First slide

Trigonometric equations

Question

General solution of equation $7 \cos^{2} θ + 3 \sin^{2} θ = 4$ is

Easy

A

$θ = n π \pm \frac{π}{6}, n \in z$
B

$θ = n π \pm \frac{π}{4}, n \in z$
C

$θ = n π \pm \frac{π}{3}, n \in z$
D

$θ = n π \pm \frac{π}{2}, n \in z$

Solution

$7 \cos^{2} θ + 3 \sin^{2} θ = 4 \Rightarrow 4 \cos^{2} θ + 3 \cos^{2} θ + 3 \sin^{2} θ = 4$
$\Rightarrow 4 \cos^{2} θ + 3 = 4 \Rightarrow 4 \cos^{2} θ = 1 \Rightarrow \cos^{2} θ = \frac{1}{4} = {(\frac{1}{2})}^{2} \Rightarrow \sin^{2} θ = \frac{3}{4} \Rightarrow \sin θ = \pm \frac{\sqrt{3}}{2}$
$\Rightarrow θ = n π \pm \frac{π}{3}, n \in z$

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