Let be fixed. If the integral dx = A(x) 2α + B(x) sin 2α + C, where C is a constant of integration then the functions A(x) and B(x) are respectively :

Engineering

Mathematics

Integration of Trigonometric Functions

Integration by Substitution

Question

Let $α \in (0, \frac{π}{2})$ be fixed. If the integral $\int \frac{tanx + tanα}{tanx - tanα}$ dx = A(x) 2α + B(x) sin 2α + C, where C is a constant of integration then the functions A(x) and B(x) are respectively :

x + α and loge |sin(z + α)|

x + α and log_e |sin(x – α)|

x – α and log_e |sin(x – α)|

x – α and log_e |cos(x – α)|

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$\int \frac{sinxcosα + cosxsinα}{sinx cosα - \cos x \sin α} dxo$

$= \int \frac{\sin (x + α)}{\sin (x - α)} dx$

$= \int \frac{\sin (x - α + 2 α)}{\sin (x - α)} dx$

$= \int \frac{\sin (x - α) \cos 2 α}{\sin (x - α)} dx + \int \frac{\cos (x - α) \sin 2 α}{\sin (x - α)} dx$

= (x – α) cos 2α + sin 2α log |sin(x – α)| + C