silemus.
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  1. 7cosθ and tanθ from sinθ
  2. 9cos75° via sum formula
  3. 11Solving 2cos²x−cosx−1=0
  4. 13Solving sin2x=cosx
  5. 16Largest angle, law of cosines
  6. 18Inverse function value
  7. 23Solving 2^(x+1)=3^x
  8. 27Roots of a cubic
  9. 29Hole vs vertical asymptote
  10. 32Sum of infinite geometric series
  11. 34Angle between two vectors
  12. 37Dividing complex numbers
  13. 38Quadratic with complex roots
  14. 39Modulus and argument of z

9cos75° via sum formula

Use a sum formula to find the exact value of cos 75°, then give it to 4 decimal places.

cos 75° = (√6 − √2)/4, which is about 0.2588. Split 75° as 45° + 30°, apply cos(A+B) = cosA cosB − sinA sinB, plug in the known values, then simplify. Checking: (2.449 − 1.414)/4 ≈ 0.2588.

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