First slide

Trigonometric transformations

Question

$\cos â¡ 22^{â} + \cos â¡ 78^{â} + \cos â¡ 80^{â} =$

Moderate

A

$4 \sin â¡ 11^{â} \sin â¡ 39^{â} \sin â¡ 40^{â}$
B

$1 + 4 \cos â¡ 11^{â} \cos â¡ 39^{â} \cos â¡ 40^{â}$
C

$1 + 4 \sin â¡ 11^{â} \sin â¡ 39^{â} \sin â¡ 40^{â}$
D

$4 \cos â¡ 11^{â} \cos â¡ 39^{â} \cos â¡ 40^{â}$

Solution

Apply the identity, if $A + B + C = 180 Â°$ then $\cos A + \cos B + \cos C$
$= 1 + 4 \sin â¡ (A / 2) \sin â¡ (B / 2) \sin â¡ (C / 2)$

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