Question

Let f(x, n) = $\int \frac{x^2 + n(n-1)}{(x \sin x + n \cos x)^2} dx$ and f(0, n) = 0. (n ∈ N; n ≥ 2)

7. If f($\frac{\pi}{3}$, 7) = tan(A - B) then $\frac{\tan A}{\tan B}$ = ___ $(0 < B < \frac{\pi}{4}, 0 < A < \frac{\pi}{2})$

• A. $\frac{7}{2}$
• B. 7
• C. $\frac{21}{2}$
• D. 14

Answer 1

Answer: (C)

$\frac{21}{2}$

Answer 2

Unfortunately, I am unable to find the solution to this question.