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koli123able

Show that the function sinx+cosx is of period 2pi. Also prove that sinx+cosx=sqrt(2)sin(x+pi/4)

  • one year ago
  • one year ago

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  1. yashar806
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    hi satellite help me after this

    • one year ago
  2. goformit100
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    i think it is C.B.S.E. Question

    • one year ago
  3. koli123able
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    \[\sqrt2\sin(x+\frac{ \pi }{ 4 })\]

    • one year ago
  4. koli123able
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    what does C.B.S.E means ?

    • one year ago
  5. koli123able
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    sinx cos pi/4 + cosx sin pi/4 what's next?

    • one year ago
  6. satellite73
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    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

    • one year ago
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  7. campbell_st
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    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 \[\sqrt{2}\sin(x + \frac{\pi}{4})\]

    • one year ago
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