$\tan \frac{1}{2}\left(\sin ^{-1} \frac{2 x}{1+x^{2}}+\cos ^{-1} \frac{1-y^{2}}{1+y^{2}}\right), |x| < 1, y > 0$ तथा $x y < 1$ में से प्रत्येक का मान ज्ञात कीजिए।
यदि $A =\left[\begin{array}{ll}\alpha & 0 \\ 1 & 1\end{array}\right] B =\left[\begin{array}{ll}1 & 0 \\ 5 & 1\end{array}\right]$, जह्ँ $A ^2= B$, तो $\alpha$ का मान है :
यदि $\left[\begin{array}{cc}x+y & y \\ 2 x & x-y\end{array}\right]\left[\begin{array}{c}2 \\ -1\end{array}\right]=\left[\begin{array}{l}3 \\ 2\end{array}\right]$ तो $x y$ बराबर होगा
यदि $A=\left[\begin{array}{ll}\alpha & 0 \\ 1 & 1\end{array}\right]$ और $B=\left[\begin{array}{ll}1 & 0 \\ 5 & 1\end{array}\right]$ तब $A^2=B$ सत्य है :
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