4 cos2 x 1 0 lessthanorequalto x 0 lessthanorequalto 2pi 2

4 cos^2 x - 1 = 0 lessthanorequalto x 0 lessthanorequalto 2pi 2 sin 2x + squareroot 3 = 0 0 lessthanorequalto x 0 lessthanorequalto 360 2 sin 2x + squareroot 3 =0 0 lessthanorequalto x 0 lessthanorequalto 2 pi 3 sin 2x - 3 cos x =0 0 lessthanorequalto x 0 lessthanorequalto 360 cos 2x + 5 = 4 sin x 0 lessthanorequalto x lessthanorequalto 360 4 tan 3x + 5 = 1 lessthanorequalto x lessthanorequalto pi 2 cos 6x + 5 = 8 5 sin2x - 6 sin x =0 3 cos 2x + cos x =-1

Solution

e)4cos²x -1=2

4cos²x =3

cos²x =3/4

cosx=-(3)/2 ,cosx=(3)/2

x=5/6,7/6 ,x=/6,11/6

x=/6,5/6,7/6,11/6

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f)0^o<=x<=360^o

0^o<=2x<=720^o

2sin2x+3=0

sin2x=(3)/2

2x=60^o,120^o,420^o,480^o

x=30^o,60^o,210^o,240^o

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g)0<=x<=2

0<=2x<=4

2sin2x+3=0

sin2x=(3)/2

2x=/3 ,2/3 ,7/3 ,8/3

x=/6 ,2/6 ,7/6 ,8/6

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h)3sin2x -3cosx =0

=>sin2x -cosx =0

=>2sinxcosx -cosx =0

=>cosx(2sinx -1)=0

=>cosx=0, sinx =1/2

=>x =90^o,270^o , x=30^o,150^o

=>x=30^o,90^o,150^o,270^o