First slide

Trigonometric Identities

Question

The least value of $2 \sin^{2} θ + 3 \cos^{2} θ$ is

Very Easy

A

1
B

2
C

3
D

5

Solution

$\begin{matrix} 2 \sin^{2} θ + 3 \cos^{2} θ = 2 (\sin^{2} θ + \cos^{2} θ) + \cos^{2} θ \\ = 2 + \cos^{2} θ \geq 2 [∵ \cos^{2} θ > 0] \end{matrix}$

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