MCQ
For all real values of $\text{x},\cot\text{x}-2\cot\text{}$ is equal to:
- A$\tan2\text{x}$
- B$\tan\text{x}$
- C$-\cot3\text{x}$
- DNone of these
Solution:
We have,
$\cot\text{x}-2\cot2\text{x}=\cot\text{x}-2\frac{\cot^2\text{x}-1}{2\cot\text{x}}$
$=\frac{1}{\cot\text{x}}$
$=\tan\text{x}$
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If $\text{y}=\frac{1+\frac{1}{\text{x}^{2}}}{1-\frac{1}{\text{x}^{2}}}$ then $\frac{\text{dy}}{\text{dx}}$ is equal to:
$\frac{-4\text{x}}{(\text{x}^{2}-1)^{2}}$
$\frac{-4\text{x}}{(\text{x}^{2}-1)^{2}}$
$\frac{1-\text{x}^{2}}{4\text{x}}$
$\frac{4\text{x}}{\text{x}^{2}-1}$