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For acute angles A and B, if $\sec (2A - B) = \sqrt{2}$ and $\operatorname{cosec} (A + B) = 2$, then find the values of A and B.
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Sol. $\sec(2A - B) = \sqrt{2} \Rightarrow 2A - B = 45^\circ$ (I Mark)
$\operatorname{cosec}(A + B) = 2 \Rightarrow A + B = 30^\circ$ (II Mark)
On solving, $A = 25^\circ, B = 5^\circ$ (III Mark)
$\operatorname{cosec}(A + B) = 2 \Rightarrow A + B = 30^\circ$ (II Mark)
On solving, $A = 25^\circ, B = 5^\circ$ (III Mark)