anonymous
  • anonymous
Simplify: (sin Θ − cos Θ)2 + (sin Θ + cos Θ)2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
A. -sin^2Θ B. -cos^2Θ c. 2 d. 0
anonymous
  • anonymous
please please help
kropot72
  • kropot72
The first step is to expand the brackets. Expanding the first bracket we get \[\large (\sin\theta-\cos\theta)^{2}=\cos^{2}\theta-2\sin\theta \cos\theta+\cos^{2}\theta\] What do you get when you expand the second bracket?

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anonymous
  • anonymous
hm not sure
anonymous
  • anonymous
please help me out real quick
kropot72
  • kropot72
The expansion of the second bracket is \[\large \sin^{2}\theta+\sin\theta \cos\theta+\cos^{2}\theta\] Now you need to collect like terms in the sum of the two expansions and simplify.
anonymous
  • anonymous
okay i understand so would the answer be A?
kropot72
  • kropot72
Please don't guess the answer. The sum of the two expansions is \[\large 2\sin^{2}\theta+2\cos^{2}\theta\] Now you need to simplify.
anonymous
  • anonymous
so how would i simplify this??
kropot72
  • kropot72
Well 2 is a common factor. So we get \[\large 2(\sin^{2}\theta+\cos^{2}\theta)\] If you know your trig identities this can be easily simplified.
kropot72
  • kropot72
What is the value of \[\large \sin^{2}\theta+\cos^{2}\theta=?\]
anonymous
  • anonymous
im not sure im terrible at this
anonymous
  • anonymous
would it equal 0 maybe?
kropot72
  • kropot72
Not really. \[\large \sin^{2}\theta+\cos^{2}\theta=1\]
anonymous
  • anonymous
so then you woiuld do 1 multiplyed by 2 and the answer would be 2?
kropot72
  • kropot72
Correct!
anonymous
  • anonymous
thank you so much
kropot72
  • kropot72
You're welcome :)

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