If \alpha and \beta are complementary angles, then which one of the following is correct?
For the following two (02) items: Let p\sin^2 \alpha + q\cos^2 \alpha = m, q\sin^2 \beta + p\cos^2 \beta = n; p \neq m, n and q \neq m, n.
- A. mn - 1 = 0
- B. mn + 1 = 0
- C. m + n = 0
- D. m - n = 0 ✓
Correct Answer: D. m - n = 0
Explanation
If \alpha and \beta are complementary, \tan \alpha \tan \beta = 1. Using the expressions for \tan^2 \alpha and \tan^2 \beta, we get \frac{m-q}{p-m} \times \frac{n-p}{q-n} = 1. Solving this yields (m-q)(n-p) = (p-m)(q-n), which simplifies to m - n = 0.
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