anonymous
  • anonymous
Show that the function sinx+cosx is of period 2pi. Also prove that sinx+cosx=sqrt(2)sin(x+pi/4)
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
hi satellite help me after this
goformit100
  • goformit100
i think it is C.B.S.E. Question
anonymous
  • anonymous
\[\sqrt2\sin(x+\frac{ \pi }{ 4 })\]

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anonymous
  • anonymous
what does C.B.S.E means ?
anonymous
  • anonymous
sinx cos pi/4 + cosx sin pi/4 what's next?
anonymous
  • anonymous
it is a consequence of the "addition angle" formula the general case is \[a\sin(x)+b\cos(x)=\sqrt{a^2+b^2}\sin(x+\theta)\] and a succinct explanation is in the attachment
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campbell_st
  • campbell_st
this requires putting into the form asin(x) + bcos(x) = Rsin(x + m) \[R = \sqrt{a^2 + b^2}\] and \[m = \tan^{-1}(\frac{a}{b})\] so\[R = \sqrt{1^2 + 1^2 } = \sqrt{2}\] \[m = \tan^{-1}(\frac{1}{1}) = \frac{\pi}{4}\] so you get \[\sqrt{2}\sin(x + \frac{\pi}{4})\]

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