Italy
If ^@ A ^@ and ^@B^@ are acute angles such that ^@cot{\space} A ^@
= ^@tan{\space} B^@, find the value of ^@(A + B )^@.
Answer:
^@90^\circ^@
- 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} @^
- Thus, the value of ^@(A + B)^@ is ^@\bf 90^\circ^@.
