A) \[\tan x+\cot x+c\]
B) \[\sec x\tan x+c\]
C) \[\cos \text{ec}x\cot x+c\]
D) None of these
Correct Answer: D
Solution :
\[\int_{{}}^{{}}{{{(\tan x-\cot x)}^{2}}dx}=\int_{{}}^{{}}{({{\tan }^{2}}x+{{\cot }^{2}}x-2)\,dx}\] \[=\int_{{}}^{{}}{{{\sec }^{2}}x\,dx}+\int_{{}}^{{}}{\text{cose}{{\text{c}}^{\text{2}}}x\,dx}-\int_{{}}^{{}}{4\,dx}\] \[=\tan x-\cot x-4x+c.\]
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