The sum of solutions of the equation cos\(\frac{cos\,x}{1+sin\,x}\)=|tan 2x|,x\(\in\)(\(-\frac{\pi}{2},\frac{\pi}{2}\))-(\(-\frac{\pi}{4},\frac{\pi}{4}\)) is:
\(-\frac{11\pi}{6}\)
\(\frac{\pi}{10}\)
\(-\frac{7\pi}{30}\)
\(-\frac{\pi}{15}\)
The correct answer is option (A) : \(-\frac{11\pi}{6}\)
If \( \alpha>\beta>\gamma>0 \), then the expression \[ \cot^{-1} \beta + \left( \frac{1 + \beta^2}{\alpha - \beta} \right) + \cot^{-1} \gamma + \left( \frac{1 + \gamma^2}{\beta - \gamma} \right) + \cot^{-1} \alpha + \left( \frac{1 + \alpha^2}{\gamma - \alpha} \right) \] is equal to:
If \[ \frac{dy}{dx} + 2y \sec^2 x = 2 \sec^2 x + 3 \tan x \cdot \sec^2 x \] and
and \( f(0) = \frac{5}{4} \), then the value of \[ 12 \left( y \left( \frac{\pi}{4} \right) - \frac{1}{e^2} \right) \] equals to: