Ответ:
Уравнение касательной : [tex]\bf y=f(x_0)+f'(x_0)(x-x_0)[/tex] .
[tex]\bf f(x)=sinx+cosx\ \ ,\ \ x_0=\pi \\\\f(\pi )=sin\, \pi +cos\, \pi =0-1=-1\\\\f'(x)=cosx-sinx\\\\f'(\pi )=cos\pi -sin\pi =-1-0=-1\\\\y=-1-1(x-\pi )\\\\\boxed{\bf \ y=-x+\pi -1\ }[/tex]
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Ответ:
Уравнение касательной : [tex]\bf y=f(x_0)+f'(x_0)(x-x_0)[/tex] .
[tex]\bf f(x)=sinx+cosx\ \ ,\ \ x_0=\pi \\\\f(\pi )=sin\, \pi +cos\, \pi =0-1=-1\\\\f'(x)=cosx-sinx\\\\f'(\pi )=cos\pi -sin\pi =-1-0=-1\\\\y=-1-1(x-\pi )\\\\\boxed{\bf \ y=-x+\pi -1\ }[/tex]