62 ASolutionA2cos2x sinx 10 21sin2x sinx 10 22sin2x sinx 10

6.2

A)

Solution

A)2cos²x -sinx -1=0

2(1-sin²x) -sinx -1=0

2-2sin²x -sinx -1=0

2sin²x +sinx -1=0

2sin²x +2sinx-sinx -1=0

2sinx(sinx +1)-1(sinx+1)=0

(sinx+1)(2sinx -1)=0

sinx =-1 ,sinx=1_/2

x=3_/2,x=_/6,5_/6

x=_/6,5_/6,3_/2,

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B)2sinx-3cotx-3cscx =0

2sinx-3cosx_/sinx-3_/sinx =0

2sin²x-3cosx-3 =0

2(1-cos²x)-3cosx-3 =0

2-2cos²x-3cosx-3 =0

2cos²x+3cosx+1 =0

(2cosx+1)(cosx+1)=0

cosx =-1_/2,cosx =-1

x =2_/3,4_/3 ,x =

x=2_/3,,4_/3

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C)sin -3cos =3

sin(1_/2) -cos(3_/2) =(3_/2)

sin(-(_/3)) =sin(_/3) ,sin(-(_/3)) =sin(2_/3) ,

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

=(2_/3),

=120^o,180^o