If tanα + sinα = m and tanα – sinα = n, then (m² – n²) equal to :यदि tanα + sinα = m तथा tanα – sinα = n हो, तो (m² – n²) बराबर है :

1. A√(mn)
2. B√(m/n)
3. C4√(mn)
4. D2√(mn)

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Correct answer: C. 4√(mn)

Explanation

m² − n² = (tanα + sinα)² − (tanα − sinα)² = 4 tanα sinα. Also mn = tan²α − sin²α = sin²α(sec²α − 1) = sin²α tan²α, so √(mn) = sinα tanα. Hence m² − n² = 4√(mn).m² − n² = (tanα + sinα)² − (tanα − sinα)² = 4 tanα sinα। साथ ही mn = tan²α − sin²α = sin²α(sec²α − 1) = sin²α tan²α, अतः √(mn) = sinα tanα। इसलिए m² − n² = 4√(mn)।