Work the correct alternative in each of the following
1. cos 40° + cos 80° + cos 160° + cos 240° =
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Work the correct alternative in each of the following
1. cos 40° + cos 80° + cos 160° + cos 240° =
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Question :
find the value of
cos40° + cos 80° + cos 160° + cos 240°
Formulas used :
Solution :
cos40° + cos 80° + cos 160° + cos 240°
⇒cos40° + cos 80° + cos (180 °-20°)+ cos (180°+60°)
[ use formula : cos (180- x) = -cosx
and cos(180+ x) = -cosx ]
⇒cos 40° + cos 80° - cos 20° - cos 60°
apply formula cos x+ cos y
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[tex] \implies \: 2 \cos( \frac{40 + 80}{2} ) \cos( \frac{40 - 80}{2} ) - \cos(20) \degree - \cos(60) \degree[/tex]
⇒2 cos 60° cos 20° - cos 20° - cos 60°
put the value of cos60°
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[tex] \implies \: 2 \times \frac{1}{2} \cos(20) \degree \: - \cos(20) \degree \: - \cos(60) \degree[/tex]
⇒cos20° - cos 20° - cos 60°
⇒ - cos 60°
[tex] \implies \: - \cos(60) \degree = - \frac{1}{2} [/tex]
Required Answer :[tex]\frac{-1}{2}[/tex]