anonymous
  • anonymous
*Trigonometric Identities*
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
cos2 y − sin2 y = 1 − 2sin2 y
anonymous
  • anonymous
its cos^2y - sin^2y= 1 - 2sin^2y
welshfella
  • welshfella
try using the identity sin^2 y + cos^2 y = 1

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anonymous
  • anonymous
so change cos^2?
anonymous
  • anonymous
sin^y = 1 - cos^2y
anonymous
  • anonymous
isnt it better to change cos so ill have all sin?
welshfella
  • welshfella
replace cos^2 y by 1 - sin^2 y on the left side
anonymous
  • anonymous
so its (1 - sin^2y) - sin^2y = 1- 2sin^2y
welshfella
  • welshfella
yes
anonymous
  • anonymous
1- 2sin^2y = 1-2siny
welshfella
  • welshfella
easy one this
anonymous
  • anonymous
huh?
welshfella
  • welshfella
- your last post was incorrect the previous one completed the proof
anonymous
  • anonymous
but shouldnt both sides be the same thing?o.O
welshfella
  • welshfella
No you have taken the left side and by using known trig identity converted it to the right side
welshfella
  • welshfella
- therefore the identity is true
anonymous
  • anonymous
1 - sin^2y) - sin^2y = 1- 2sin^2y
anonymous
  • anonymous
from here I expanded the brackets and got 1 - sin^2y - sin^2y = 1- 2sin^2y
anonymous
  • anonymous
- sin^2y - sin^2y = - 2 sin^2y
anonymous
  • anonymous
right??
welshfella
  • welshfella
cos^2y - sin^2y = 1 - 2sin^2y now cos^2 y = 1 - sin^2 y so substituting 1 - sin^2 y - sin^2 y = 1 - 2 sin^2 y = RHS
welshfella
  • welshfella
yes
welshfella
  • welshfella
RHS = right hand side
anonymous
  • anonymous
so then wouldnt it be 1 - 2sin^2y = 1 - 2sin^2y??
welshfella
  • welshfella
no - no need to write that usually with these , you pick the more complicated side of the identity and try to convert it to the other side . Once that is done you have confirmed the identity.
anonymous
  • anonymous
so wat will the answer be then? o.O
welshfella
  • welshfella
just write what i have put or if you like at the end write 'the above proves the original identity'.
welshfella
  • welshfella
- thats what this is - a Proof.
anonymous
  • anonymous
so this is the answer? 1 - sin^2 y - sin^2 y = 1 - 2 sin^2 y = RHS
welshfella
  • welshfella
No there are 2 lines before that - check 6 posts back.
welshfella
  • welshfella
the answer is the whole process of proving the identity
welshfella
  • welshfella
cos^2y - sin^2y = 1 - 2sin^2y now cos^2 y = 1 - sin^2 y so substituting 1 - sin^2 y - sin^2 y = 1 - 2 sin^2 y = RHS The above proves the original identity
welshfella
  • welshfella
you could also make a note to clarify that RHS = right hand side
welshfella
  • welshfella
gotta go - hope this has clarified things

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