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Verify the trigonometric identity (1 + cot A - cosec A)(1 + tan A + sec A) = 2. Which statement is correct?

1. The identity is true for all A where the functions are defined
2. The identity holds only for A = pi/4
3. The product equals 0, not 2
4. The product equals sec A * cosec A

Correct answer: The identity is true for all A where the functions are defined

Solution

Converting to sine and cosine and using (sinA+cosA)² - 1 = 2 sinA cosA, the product simplifies exactly to 2 for all admissible A.

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