Question

If A + B + C = ${180}^o$ then sin (A + B)=

• A. $-\sin C$
• B. $\cos C$
• C. $\sin C$
• D. $-\cos C$

Answer 1

Answer: (C)

$\sin C$

We have $A+B+C={180}^{\circ }$

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

$\Rightarrow \sin (A+B)=\sin ({180}^{\circ }-C)=\sin C$ since ${180}^{\circ }-\theta$ is in second quadrant , by ASTC rule, $\sin ({180}^{\circ }-\theta )$ is positive.