63 ASolutionAsin2xcosxcos2xsinx 22 sin2xx22 sin3x22 0

6.3

A)sin2xcosx+cos2xsinx =2_/2

sin(2x+x)=2_/2

sin(3x)=2_/2

0<=x<2 ==>0<=3x<6

3x=_/4,3_/4,9_/4,11_/4,17_/4,19_/4,

x=_/12,3_/12,9_/12,11_/12,17_/12,19_/12,

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B)sin5xcos3x+cos5xsin3x =1

sin(5x+3x)=1

sin8x =1

8x =2k +(_/2)

x =(k_/4) +(_/16)

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C)cos³4x =-1

cos4x =-1

4x =2k +

x=(k_/2)+(_/4)