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Which of the following trigonometric expressions simplifies to 1?

1. (1 - 2*sin²(A)) / (2*cot(pi/4 + A)*cos²(pi/4 - A))
2. sin(pi - A)/(sin(A) - cos(A)*tan(pi/2)) + cos(pi - A)
3. 1/(4*sin²(A)*cos²(A)) + (1 - tan²(A))²/(4*tan²(A))
4. (1 + sin(2A))/(sin(A) + cos(A))²

Correct answer: (1 + sin(2A))/(sin(A) + cos(A))²

Solution

Option D directly simplifies to 1 because the numerator 1+sin(2A) equals (sinA+cosA)², which is exactly the denominator.

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