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Period of f(x)=sin((cosx)+x) is...

Period of `f(x)=sin((cosx)+x)` is

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`f(x)=sin(x+cosx)`
Let period be T.
` :. f(x+T)=f(x)` for all real x.
Putting `x=0`, we have
`f(T)=f(0)`
or ` sin(T+cos T)=sin 1`
By intelligent guessing, `T=2pi`, which is the least positive value.
Also, `f(x+2pi)=sin(x+2pi +cos(x+2pi))`
`=sin(2pi+(x+cosx))`
`=sin(x+cosx)=f(x)`
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