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In triangle ABC the angle C is a right angle and sinA = 3/5. The value of sinA·sinB + cosA·cosB is:

Competition practiceTrigonometry
  • A1
  • B24/25
  • C12/25
  • D0

Step-by-Step Solution

With C = 90° the other two angles are complementary, so B = 90° − A, giving sinB = cosA = 4/5 and cosB = sinA = 3/5. The expression becomes (3/5)(4/5) + (4/5)(3/5) = 12/25 + 12/25 = 24/25 = 0.96 (the triangle is the 3-4-5 one, A ≈ 36.87°). Stopping after one of the two equal products gives 12/25; putting a minus sign between them turns the expression into cos(A + B) = cos90° = 0; and reading it as cos(A − B) and assuming A = B gives 1, which would need A = B = 45°.
Answer: B) 24/25

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