Multiple choice general knowledge math & puzzles

If a=sinA , b=cosA then (a+b)^2 + (a-b)^2

  1. 4sinAcosA

  2. -4sinAcosA

  3. 2

  4. 0
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Expanding (sinA+cosA)²+(sinA-cosA)² gives sin²A+2sinAcosA+cos²A+sin²A-2sinAcosA+cos²A = 2(sin²A+cos²A) = 2(1) = 2, using the fundamental identity sin²θ+cos²θ=1.

AI explanation

Expanding both squares: (a+b)^2 + (a-b)^2 = 2a^2 + 2b^2 = 2(a^2+b^2). Since a=sinA and b=cosA, sin^2A + cos^2A = 1 by the Pythagorean identity, so the expression equals 2*1 = 2.

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