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 :
- cos (180-x ) = -cosx
- cos (180+ x) = -cosx
- cos(-x) = cosx
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
________________________
⇒2 cos 60° cos 20° - cos 20° - cos 60°
put the value of cos60°
_______________________
⇒cos20° - cos 20° - cos 60°
⇒ - cos 60°
Required Answer :
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