Question

$\int \frac { \sec x \cdot \operatorname { cosec } x } { 2 \cot x - \sec x \operatorname { cosec } x }$dx is equal to

• A. $\frac{1}{2}$ln | sec2x + tan2x | + C
• B. ln | sec x + cosec x | + C
• C. ln | sec x + tan x | + C
• D. $\frac{1}{2}$ln | sec x + cosec x | + C

Answer 1

Answer: (A)

$\frac{1}{2}$ln | sec2x + tan2x | + C

Answer 2

$\int \frac { \sec x \operatorname { cosec } x } { 2 \cot x - \sec x \operatorname { cosec } x } d x = \int \frac { d x } { 2 \cos ^ { 2 } x - 1 }$

= ln | sec2x + tan2x | + C