First slide

Extreme values and Periodicity of Trigonometric functions

Question

If $\sin^{2} θ_{1} + \sin^{2} θ_{2} + \sin^{2} θ_{3} \geq 0$ then which of the following is not the possible
value of $\cos θ_{1} + \cos θ_{2} + \cos θ_{3}$ ?

Moderate

A

-3
B

3
C

-1
D

-2

Solution

$L e t \sin^{2} θ_{1} = \sin^{2} θ_{2} = \sin^{2} θ_{3} = 0$
$\begin{array}{l} \Rightarrow θ_{1} = θ_{2} = θ_{3} = 0, π, 2 π \\ \Rightarrow \cos θ_{1} = \pm 1, \cos θ_{2} = \pm 1, \cos θ_{3} = \pm 1 \\ \Rightarrow \cos θ_{1} + \cos θ_{2} + \cos θ_{3} = 1, - 1, 3, - 3 b u t \neq - 2 \end{array}$

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