anonymous
  • anonymous
Simplify: (sin Θ − cos Θ)^2 + (sin Θ + cos Θ)^2. Options include: -sin^2 Θ -cos^2Θ 0 2
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
So what would you get should you foil out both of those?
anonymous
  • anonymous
Ok I'm going to let sin Θ = x and cos Θ = y (x-y)(x-y) (x^2-xy+y^2) (x+y)(x+y) (x^2 +xy+y^2)
anonymous
  • anonymous
so (sin Θ^2 - sin Θ times cos Θ + cos Θ^2) + (sin Θ^2 + sin Θ times cos Θ + cos Θ^2) but what is sin theta times cos theta??

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anonymous
  • anonymous
Well, you should have a \(-2\sin(\theta)\cos(\theta)\) and a \(+2\sin(\theta)\cos(\theta)\), so those would cancel anyway, we don't need to worry about them.
anonymous
  • anonymous
ohh I forgot the outside values
anonymous
  • anonymous
But once you cancel and combine everything, you would have \(2\sin^{2}(\theta) + 2\cos^{2}(\theta) = 2(\sin^{2}(\theta) + \cos^{2}(\theta))\)
anonymous
  • anonymous
Okay so it should be (sin^2 theta + cos^2 theta) + (sin^2 theta + cos^2 theta)? And the pythagorean identity says that sin^2 theta + cos^2 theta = 1, so 1 + 1 = 2?
anonymous
  • anonymous
Yep :)
anonymous
  • anonymous
Thank you so much!
anonymous
  • anonymous
Yep, no problem :3
xapproachesinfinity
  • xapproachesinfinity
i have seen this question here over and over lol did teacher run out of problems or something hehe
xapproachesinfinity
  • xapproachesinfinity
teachers*

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