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