Passage \( \quad: \) It is given that \( A=\left(\tan ^{-1} x\right)^{3}+\left(\cot ^{-1} x\righ... VIDEO
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 \( -1 \leq x \leq 1 \& \) \( \tan ^{-1} x+\cot ^{-1} x=\frac{\pi}{2} \forall x \in R \)
Maximum value of \( B \) is
(a) \( \frac{\pi^{2}}{8} \)
(b) \( \frac{\pi^{2}}{16} \)
(c) \( \frac{\pi^{2}}{4} \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions 2023-06-08 If maximum value of \( \tan ^{-1} x+2 \sin ^{-1} x+3 \sec ^{-1} x \) is \( \frac{p \pi}{q} \) wh... 2023-06-08 The number of ordered pairs \( (x, y) \) satisfying \( |y|=\cos x \) and \( y=\sin ^{-1}(\sin x)... 2023-06-08 Passage \( \quad \) : It is given that \( A=\left(\tan ^{-1} x\right)^{3}+\left(\cot ^{-1} x\rig... 2023-06-08 Absolute difference of greatest \& least value of \( \cos ^{-1} x^{2} \) \( \left(x \in\left[\fr... 2023-06-08 \( \tan ^{-1} n, \tan ^{-1}(n+1) \) and \( \tan ^{-1}(n+2), n \in N \), are angles of a triangle... 2023-06-08 If the range of \( m \) for which the equation \( \operatorname{cosec}^{-1} x=m x \) has exactly... 2023-06-08 Passage \( \quad: \) Let us define here three functions in the domain of \( [-1,1], f(x)=\sin ^{... 2023-06-08 Passage \( \quad: \) Let us define here three functions in the domain of \( [-1,1], f(x)=\sin ^{... 2023-06-08 Match the statement in Column-I with statements in Column-II.
\begin{tabular}{|l|l|l|l|}
\hline ... 2023-06-08 Passage \( \quad: \) Let us define here three functions in the domain of \( [-1,1], f(x)=\sin ^{... 2023-06-08 Passage \( \quad: \) It is given that \( A=\left(\tan ^{-1} x\right)^{3}+\left(\cot ^{-1} x\righ... 2023-06-08 Match the statement in Column-I with statements in Column-II.
\begin{tabular}{|l|l|l|l|}
\hline ... 2023-06-08 Passage \( \quad: \) It is given that \( A=\left(\tan ^{-1} x\right)^{3}+\left(\cot ^{-1} x\righ... 2023-06-08 If \( f(x)=\left(\sin ^{-1} x\right)^{2}+\left(\cos ^{-1} x\right)^{2} \), then:
(a) \( f(x) \) ... 2023-06-08 If \( \alpha, \beta \) are the roots of the equation \( 6 x^{2}+11 x+3=0 \), then -
(a) Both \( ... 2023-06-08 Let \( f(x)=\sin ^{-1} x+\cos ^{-1} x \). Then \( \frac{\pi}{2} \) is equal to:
(a) \( f\left(-\... 2023-06-08 \( \sum_{n=1}^{\infty} \tan ^{-1} \frac{4 n}{n^{4}-2 n^{2}+2} \) is equal to:
(a) \( \tan ^{-1} ... 2023-06-08 The function \( f(x)=\cos ^{-1} x+\cos ^{-1}\left(\frac{x}{2}+\frac{\sqrt{3-3 x^{2}}}{2}\right) ... 2023-06-08 Number of the integers not satisfying in the domain of the function \( \sin ^{-1}\left[\frac{2}{... 2023-06-08 Let \( m \) be the number of elements in the domain of \( f(x) \) where \( f(x)=\sin ^{-1}\left[... 2023-06-08 Number of integral values of \( k \) for which the equation \( 4 \cos ^{-1}(-|x|)=k \) has exact...