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sin(3x-16)=cos(4x-6) x=?

Sagot :

AyaZ
[tex]sin(3x-16)=cos(4x-6) \\ sin(3x-16)=sin( \frac{ \pi }{2} -(4x-6)) \\ 3x-16=\frac{ \pi }{2} -(4x-6)[/tex]
[tex]3x-16=\frac{ \pi }{2} -4x+6[/tex]
then :
[tex]3x-16=2k \pi +(\frac{ \pi }{2} -4x+6) \\ 7x=2k \pi +\frac{ \pi }{2}+22 \\ x= \frac{2k \pi}{7} +\frac{ \pi }{14}+ \frac{22}{7} [/tex]
[tex]and \\ 3x-16=2k \pi + \pi -(\frac{ \pi }{2} -4x+6) \\ 3x-16=2k \pi + \pi -\frac{ \pi }{2} +4x-6 \\ -x=2k \pi + \frac{ \pi }{2}+10 \\ x=-2k \pi - \frac{ \pi }{2}-10[/tex]
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