If sec A = (m² + n²)/(m² − n²), find the value of tan A.
Show answer & explanation
Correct answer: A
Explanation
secA = (m² + n²)/(m² − n²)
tan²A = sec²A − 1
sec²A = (m² + n²)²/(m² − n²)²
tan²A = [(m² + n²)² − (m² − n²)²] / (m² − n²)²
= [ (m⁴ + 2m²n² + n⁴) − (m⁴ − 2m²n² + n⁴) ] / (m² − n²)²
= (4m²n²)/(m² − n²)²
⇒ tanA = 2mn/(m² − n²)