question_answer

If \[\Delta \text{ }ABC\] is right angled at By what is the value of \[\sin \,(A+C)\].

Answer:

\[\angle B=90{}^\circ \]                         [Given]

We know that in \[\Delta \text{ }ABC\],

\[\angle A+\angle B+\angle C=180{}^\circ \]                   [Angle sum property of a \[\Delta \]]

\[\Rightarrow \,\,\angle A+\angle C+90{}^\circ =180{}^\circ \]

\[\Rightarrow \,\,\angle A+\angle C=180{}^\circ -90{}^\circ \]

\[=90{}^\circ \]

\[\therefore \sin (A+C)=sin\,90{}^\circ =1\]