anonymous
  • anonymous
what is another expression for cos x-sin x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
options A \[\sqrt{2} \cos \left( x+\frac{ \pi }{ 4 } \right)\]
anonymous
  • anonymous
\[\sqrt{2}\cos \left( x-\frac{ \pi }{ 4} \right)\]
anonymous
  • anonymous
C \[2\cos \left( x+\frac{ \pi }{ 4} \right)\]

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anonymous
  • anonymous
D \[2\cos \left( x-\frac{ \pi}{ 4 } \right)\]
anonymous
  • anonymous
please help!!!
anonymous
  • anonymous
@ganeshie8
Michele_Laino
  • Michele_Laino
hint: if I multiply and divide the left side by sqrt(2), I get this: \[\Large \sqrt 2 \left( {\frac{1}{{\sqrt 2 }}\cos x - \frac{1}{{\sqrt 2 }}\sin x} \right)\]
Michele_Laino
  • Michele_Laino
now, please keep in mind that: \[\Large \frac{1}{{\sqrt 2 }} = \cos \left( {\frac{\pi }{4}} \right) = \sin \left( {\frac{\pi }{4}} \right)\]
Michele_Laino
  • Michele_Laino
hint: \[\Large \begin{gathered} \cos x - \sin x = \sqrt 2 \left( {\frac{1}{{\sqrt 2 }}\cos x - \frac{1}{{\sqrt 2 }}\sin x} \right) \hfill \\ \hfill \\ = \sqrt 2 \left( {\cos \left( {\frac{\pi }{4}} \right)\cos x - \sin \left( {\frac{\pi }{4}} \right)\sin x} \right) \hfill \\ \end{gathered} \]
anonymous
  • anonymous
ok,, 10nks.. but still stuck on how to simplify further
Michele_Laino
  • Michele_Laino
we can apply this identity: \[\Large \cos \left( {\alpha + \beta } \right) = \cos \alpha \cos \beta - \sin \alpha \sin \beta \]
anonymous
  • anonymous
ok so that'll be \[\sqrt{2}(\cos(x+\frac{ \pi }{ 4}))\]
Michele_Laino
  • Michele_Laino
that's right!
anonymous
  • anonymous
so the correct answer will be A
Michele_Laino
  • Michele_Laino
yes! it is option A)
anonymous
  • anonymous
oh ok,, thank u very much..
Michele_Laino
  • Michele_Laino
:)

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