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Evaluate the following: cos 20°. cos 40°. cos 60°. cos 80°

Evaluate the following: cos 20°. cos 40°. cos 60°. cos 80°

Grade:11

1 Answers

Harshit
31 Points
5 years ago
Let
P=cos20.cos40.cos60.cos80
Q= sin20.sin40.sin60.sin80
 
P.Q= (sin20.cos20).(sin40.cos40)(sin60.cos60)(sin80.cos80)
P.Q=  1/16 (sin40.sin80.sin120.sin160)        [sinA.cosA= sin2A/2]
P.Q= 1/16 (sin20.sin40.sin60.sin80)            [sin120=sin(180-60)=sin60  ,  sin160=sin(180-20)=sin20
P.Q= 1/16 Q
P= 1/16
so the value of
cos20.cos40.cos60.cos80=1/16

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