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Which one of the following statements is TRUE?

Competition practiceTrigonometry
  • Asin(A + B) = sinA + sinB for all angles A and B
  • Bcos60° = 2co30° − 1
  • Ctan(A + B) = tanA + tanB for all angles A and B
  • Dsin2A = 2sinA for all angles A

Step-by-Step Solution

The double-angle form cos2A = 2co with ° gives 2(3/4) − 1 = 1/2 = cos60°, so that statement is true. Sine, tangent and the double angle are not additive: for example sin(30° + 60°) = 1 while sin30° + sin60° ≈ 1.366.
Answer: B) cos60° = 2co30° − 1

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