MTALHAHASSAN2
  • MTALHAHASSAN2
Need help!! 2. Give that cos (x+y) = cos x cos y – sin x sin y, use this to express cos 2x in terms of cos x
Mathematics
schrodinger
  • schrodinger
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campbell_st
  • campbell_st
so replace y with x so you have cos(x + x) = cos(x)cos(x) - sin(x)sin(x) and simplify from there.
campbell_st
  • campbell_st
so the left side of the equation becomes cos(2x)
MTALHAHASSAN2
  • MTALHAHASSAN2
why do you do that

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campbell_st
  • campbell_st
now you can simplify the right side
MTALHAHASSAN2
  • MTALHAHASSAN2
I mean why do you change the y into x
campbell_st
  • campbell_st
that way when you replace y with x cos(x + y) = cos(x + x) which is cos(2x)
MTALHAHASSAN2
  • MTALHAHASSAN2
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MTALHAHASSAN2
  • MTALHAHASSAN2
right
campbell_st
  • campbell_st
thats correct.... but the question asks in terms of cos(x) so what do you know about sin^2(x)..?
MTALHAHASSAN2
  • MTALHAHASSAN2
sin2x = 2sinx cosx
campbell_st
  • campbell_st
no its \[\sin^2(x) \]
MTALHAHASSAN2
  • MTALHAHASSAN2
is there is any formula for this
MTALHAHASSAN2
  • MTALHAHASSAN2
I don't have it for this one I have for Sin2x
campbell_st
  • campbell_st
sure its one of the fundamentals \[\cos^2(x) + \sin^2(x) = 1\]
MTALHAHASSAN2
  • MTALHAHASSAN2
oh know it be sin^2 (x) = 1-cos^2x
MTALHAHASSAN2
  • MTALHAHASSAN2
= cos^2 x -(1-cos^2 x)
MTALHAHASSAN2
  • MTALHAHASSAN2
MTALHAHASSAN2
  • MTALHAHASSAN2

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