Evaluate the following: cos 20°. cos 40°. cos 60°. cos 80°
Derwin Saldanha , 8 Years ago
Grade 11
Trigonometry> Evaluate the following: cos 20°. cos 40°....
1 AnswersHarshit
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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