Question

$\int {(tanx-cotx)}^{2}dx$ =

• A. $tanx$ $+$ $x$ $+$ $c$
• B. $tanx$ $-$ $x$ $+$ $c$
• C. $tanx$ $-$ $cotx$ $+$ $c$
• D. $tanx$ $-$ $cotx$ $-4x$ $+c$

Answer 1

The correct option is D $tanx$ $-$ $cotx$ $-4x$ $+c$

$\int (\tan x-\cot x{)}^{2}dx$

$=\int ({\tan }^{2}x+{\cot }^{2}x-2\tan x\cot x)dx$

$=\int \left(\right({\sec }^{2}x-1)+(cose{c}^{2}x-1)-2)dx$

$\int ({\sec }^{2}x+cose{c}^{2}x-4)dx$

$=\tan x-\cot x-4x+c$.