what is the value of 2cos20°
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Given : x + 1/x= 2 cos20 => ( x + 1/x)3 = 8 cos3 20
=> x3 + 1/x3 + 3( x + 1/x) = 8 cos3 20
=> x3 + 1/ x3 + 3( 2cos 20)= 8 cos3 20 ( using :given value of x + 1/x= 2cos20)
=> x3 + 1/ x3= 8cos3 20 -6 cos20=2(4cos3 20-3cos20)=2 cos (3.20)=2 cos60=2.(1/2)=1
Ans. =1
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