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anonymous

  • one year ago

Simplify: (sin Θ − cos Θ)2 + (sin Θ + cos Θ)2

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  1. anonymous
    • one year ago
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    A. -sin^2Θ B. -cos^2Θ c. 2 d. 0

  2. anonymous
    • one year ago
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    please please help

  3. kropot72
    • one year ago
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    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?

  4. anonymous
    • one year ago
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    hm not sure

  5. anonymous
    • one year ago
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    please help me out real quick

  6. kropot72
    • one year ago
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    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.

  7. anonymous
    • one year ago
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    okay i understand so would the answer be A?

  8. kropot72
    • one year ago
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    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.

  9. anonymous
    • one year ago
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    so how would i simplify this??

  10. kropot72
    • one year ago
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    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.

  11. kropot72
    • one year ago
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    What is the value of \[\large \sin^{2}\theta+\cos^{2}\theta=?\]

  12. anonymous
    • one year ago
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    im not sure im terrible at this

  13. anonymous
    • one year ago
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    would it equal 0 maybe?

  14. kropot72
    • one year ago
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    Not really. \[\large \sin^{2}\theta+\cos^{2}\theta=1\]

  15. anonymous
    • one year ago
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    so then you woiuld do 1 multiplyed by 2 and the answer would be 2?

  16. kropot72
    • one year ago
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    Correct!

  17. anonymous
    • one year ago
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    thank you so much

  18. kropot72
    • one year ago
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    You're welcome :)

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