MCQ
$\tan A + \cot (180^\circ + A) + \cot (90^\circ + A) + \cot (360^\circ - A)$
- ✓$0$
- B$2\tan A$
- C$2\cot A$
- D$2(\tan A - \cot A)$
$ = \tan A + \cot A - \tan A - \cot A = 0$.
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$\lim _{t \rightarrow x} \frac{f(x) \sin t-f(t) \sin x}{t-x}=\sin ^2 x \text { for all } x \in(0, \pi)$
If $f \left(\frac{\pi}{6}\right)=-\frac{\pi}{12}$, then which of the following statement(s) is (are) TRUE?
$(A)$ $f \left(\frac{\pi}{4}\right)=\frac{\pi}{4 \sqrt{2}}$
$(B)$ $f(x)<\frac{x^4}{6}-x^2$ for all $x \in(0, \pi)$
$(C)$ There exists $\alpha \in(0, \pi)$ such that $f ^{\prime}(\alpha)=0$
$(D)$ $f ^{\prime \prime}\left(\frac{\pi}{2}\right)+ f \left(\frac{\pi}{2}\right)=0$