If ^@ A ^@ and ^@B^@ are acute angles such that ^@cot{\space} A ^@ = ^@tan{\space} B^@, find the value of ^@(A + B )^@.


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Answer:

^@90^\circ^@

Step by Step Explanation:
  1. We are told that @^ \begin{aligned} &cot{\space} A = tan{\space} B \\ {\implies}& cot{\space} A = cot{\space} (90^\circ - B) \\ {\implies}& A = 90^\circ - B &&[\because A{\space}{\space} and {\space}{\space}(90^\circ - B ){\space} are{\space} acute. ] \\ {\implies}& A + B = 90^\circ \end{aligned} @^
  2. Thus, the value of ^@(A + B)^@ is ^@\bf 90^\circ^@.

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