Question

x + 1/x = 2cosA, then x^3 + 1/x^3 =?​

Answer 1

x+1/x=2cosA

(x+1/x)³=(2cosA)³

x³+1/x³+3×x×1/x(x+1/x)=8cos³A

x³+1/x³=8cos³A-3(2cosA)

=8cos³A-6cosA

=2(4cos³A-3cosA)

=2cos3A

{cos3A=4cos³A-3cosA}formula

hope its help u...✌✌✌✌✌✌✌✌

Answer 2

given x+1/x=2cosA

do cube on both side

x^3 +1/x^3 +3 × x × 1/x( x+1/x) = 8cos^3A

x^3 + 1/x^3 +3 ×2cosA = 8cos^3A

x^3 + 1/x^3 =8cos^3A - 6cosA