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soldi70 [24.7K]
3 years ago
10

Simplify [2 (cos 210 + i sin 210)]^2

Mathematics
1 answer:
Andru [333]3 years ago
4 0
2{(cos^210+isin^210)}^2

2(cos^210-sin^10+2i*cos10*sin10)

2(cos20+i*sin20)

cos^2Ф-sin^2Ф=cos2Ф and 2sinФcosФ=sin2Ф here Ф=10°

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MARKIN BRAINIEST!!! GIVIN 30PTS!!!
Sedbober [7]

Answer:

  • (-16x² +10x -3) +(4x² -29x -2)
  • (2x² -11x -9) -(14x² +8x -4)
  • 2(x -1) -3(4x² +7x +1)

Step-by-step explanation:

I find it takes less work if I can eliminate obviously wrong answers. Toward that end, we can consider the constant terms only:

  1. -3 +(-2) = -5 . . . . possible equivalent
  2. -10 -5 = -15 . . . . NOT equivalent
  3. 3(-5) -2(5) = -25 . . . . NOT equivalent
  4. -9 -(-4) = -5 . . . . possible equivalent
  5. -7 -(-5) = -2 . . . . NOT equivalent
  6. 2(-1) -3(1) = -5 . . possible equivalent

Now, we can go back and check the other terms in the candidate expressions we have identified.

  1. (-16x² +10x -3) +(4x² -29x -2) = (-16+4)x² +(10-29)x -5 = -12x² -19x -5 . . . OK

  4. (2x² -11x -9) -(14x² +8x -4) = (2-14)x² +(-11-8)x -5 = -12x² -19x -5 . . . OK

  6. 2(x -1) -3(4x² +7x +1) = -12x² +(2 -3·7)x -5 = -12x² -19x -5 . . . OK

All three of the "possible equivalent" expressions we identified on the first pass are fully equivalent to the target expression. These are your answer choices.

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