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Question

Show that :Cos24°+Cos55°+Cos125°+Cos204°+Cos300°=12


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Solution

To prove that :Cos24°+Cos55°+Cos125°+Cos204°+Cos300°=12

L.H.S =Cos24°+Cos55°+Cos125°+Cos204°+Cos300°

=Cos24°+Cos55°+Cos(180°-55°)+Cos(180°+24°)+Cos(270°+30°)

=Cos24°+Cos55°Cos55°Cos24°+Sin30°[cos(180°-x)=-cosx,cos(180°+x)=-cosx,cos(270°+x)=sinx]

=Sin30°

=12

=RHS

Thus,Cos24°+Cos55°+Cos125°+Cos204°+Cos300°=12.

Hence proved.


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