Question

If $\Delta ABC$ is right angled at B, what is the value of $sin(A+C)$

Answer 1

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

We know that in $\Delta ABC$,

$\angle A+\angle B+\angle C={180}^{\circ }$ [Sum of angles in a triangle is ${180}^{\circ }$ ]

$\Rightarrow \angle A+\angle C+{90}^{\circ }={180}^{\circ }$

$\Rightarrow \angle A+\angle C={180}^{\circ }-{90}^{\circ }$

$={90}^{\circ }\therefore sin(A+C)=sin{90}^{\circ }=1$