Solve Cos2xcosx1 Solve Cos2xcosx1 Cos2xcosx1Solutioncos2xcos

Solution

cos(2x)-cos(x)=1

(2cos²(x)-1)-cos(x)=1

2cos²(x) -cos(x) -2=0

using quadratic formula

cos(x)=[-(-1) +[(-1)²-4(2)(-2)]]_/(2*2),cos(x)=[-(-1) -[(-1)²-4(2)(-2)]]_/(2*2)

cos(x)=[1 +[1+16]]_/4,cos(x)=[1 -[1+16]]_/4

cos(x)=(1+17)_/4,cos(x)=(1 -17)_/4

cos(x)=(1+17)_/4 , no solution

cos(x)=(1 -17)_/4

x=2n-cos^-1((1 -17)_/4),x=2n-cos^-1((1 -17)_/4) where n is an integer