Question
Download Solution PDFIf 3x = sec A and \(\frac{3}{x}\) = tan A then 9 (x2 - \(\frac{1}{x^2}\)) is ______.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
3x = sec A and \(\frac{3}{x}\) = tan A
Formula used
sec2 A - tan2 A = 1
Calculation
3x = sec A
Squaring both sides:
9x2 = sec2 A ..(1)
3/x = tan A
Squaring both sides:
9/x2 = tan2 A ..(2)
Subtracting 2 from 1.
⇒ 9x2 - 9/x2 = sec2 A - tan2 A
⇒ 9(x2 - 1/x2) = 1
The answer is 1.
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