Question

In a right angled triangle $ABC$, right angled at $C$, the value of $\sin A\cos B+\cos A\sin B$ is

• A. 5
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is B 1

In triangle $ABC$, we have
$(A+B+C)={180}^o$

Given that $\angle C={90}^o$
Therefore, $(A+B)={180}^o-{90}^0={90}^o$
$\Rightarrow \sin A.\cos B+\cos A.\sin B=\sin (A+B)=\sin \frac{\pi }{2}=1$