Duration: 14:24

0 views

0

Passage \( \quad \) : It is given that \( A=\left(\tan ^{-1} x\right)^{3}+\left(\cot ^{-1} x\right)^{3} \), where \( x0 \& B=\left(\cos ^{-1} t\right)^{2}+\left(\sin ^{-1} t\right)^{2} \),
where \( t \in\left[0, \frac{}{\sqrt{2}}\right] \& \sin ^{-1} x+\cos ^{-1} x=\frac{\pi}{2} \) for \( -1 \leq x \leq 1 \& \) \( \tan ^{-1} x+\cot ^{-1} x=\frac{\pi}{2} \forall x \in R \)
If least value of \( A \) is \( \lambda \) \& maximum value of \( B \) is \( \mu \) then \( \cot ^{-1}\left(\cot \left(\frac{\lambda-\mu \pi}{\mu}\right)\right)= \)
(a) \( \frac{\pi}{8} \)
(b) \( \frac{-\pi}{8} \)
(c) \( \frac{7 \pi}{8} \)
(d) \( \frac{-7 \pi}{8} \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live