Question

$\int_{}^{}{\sec\left( x–\frac{\pi}{3} \right)}\sec\left( x–\frac{\pi}{6} \right)$dx =

• A. $\log\left| \frac{\cos(x–\pi/3)}{\cos(x–\pi/6)} \right| + C$
• B. $2\log\left| \frac{\cos(x–\pi/3)}{\cos(x–\pi/6)} \right| + C$
• C. $2\log\left| \frac{\cos(x–\pi/6)}{\cos(x–\pi/3)} \right| + C$
• D. $\log\left| \frac{\cos(x–\pi/6)}{\cos(x–\pi/3)} \right| + C$

Answer 1

Answer: (B)

$2\log\left| \frac{\cos(x–\pi/3)}{\cos(x–\pi/6)} \right| + C$

Answer 2

= $\frac { 1 } { \sin \pi / 6 }$ $\int \frac { \left\{ \sin \left( x - \frac { \pi } { 6 } \right) - \left( x - \frac { \pi } { 3 } \right) \right\} } { \cos \left( x - \frac { \pi } { 3 } \right) \cos \left( x - \frac { \pi } { 6 } \right) } d x$

= 2

= 2$\int \left\{ \tan \left( x - \frac { \pi } { 6 } \right) - \tan \left( x - \frac { \pi } { 3 } \right) \right\} d x$

= 2

= 2log$\left| \frac { \cos \left( x - \frac { \pi } { 3 } \right) } { \cos \left( x - \frac { \pi } { 6 } \right) } \right|$+C