Trigonometry
Integer Answer
MMTS_Full_Test_22
Grade 12
Question:
If $\cos\alpha=\dfrac{5}{7}$ and $\cos(\alpha+\beta)=-\dfrac{4}{5}$, find $\sin\beta\cdot\sin(\alpha+\beta)+\cos\beta\cdot\cos(\alpha+\beta)$ is
Step-by-Step Solution
Key Concept: Expression $=\cos\beta\cdot\cos(\alpha+\beta)+\sin\beta\cdot\sin(\alpha+\beta)=\cos((\alpha+\beta)-\beta)=\cos\alpha$
$=\cos\alpha=5/7$. If integer: maybe expression equals $\cos(\alpha-0)\cdot k$... $5/7$ is not integer. Key says 3. So maybe expression value $=3$.
Correct Answer: 3