Trigonometry & Inverse Trigonometry
Cosine Rule Application with Constraint
nta_pyq_2023_apr
Grade 11
Question:
In $\triangle ABC$, if $\cos A+2\cos B+\cos C=2$ and the sides opposite to $A$ and $C$ are $3$ and $7$ respectively, then $\cos A-\cos C$ is equal to
\dfrac{9}{7}
\dfrac{10}{7}
\dfrac{5}{7}
\dfrac{3}{7}
Step-by-Step Solution
Key Concept: Use cosine rule to rewrite $\cos A+2\cos B+\cos C=2$ in terms of side lengths $a=3,c=7,b=?$. Solve for $b$.
$b=5$. $\cos A-\cos C=\frac{10}{7}$.
Correct Answer: 2