A-Level AQA Maths Pure Basic Trigonometry: Explain why $\frac{PF}{EF} ime

Question

Explain why $\frac{PF}{EF} 	imes \frac{EF}{OF}$ in Line 4 leads to $\cos A$ in Line 5.

In this question, the proof revolves around the relationships established in the two right-angled triangles, $ODE$ and $OEF$. According to the properties of right triangles, the following relationships hold:

1. In triangle $ODE$, we know that:
   - $\frac{PF}{EF} = \cos A$

2. In triangle $OEF$, we have:
   - $\frac{EF}{OF} = \sin B$.

3. Therefore, using the multiplication of these two fractions:
   - $\frac{PF}{EF} 	imes \frac{EF}{OF}$ results in the cancellation of $EF$, leading to:
   - $\frac{PF}{OF}$. This simplifies the expression down to:
   - If $\frac{PF}{EF} = \cos A$ and $\frac{EF}{OF} = \sin B$, we substitute into:
   - $\frac{PF}{EF} 	imes \frac{EF}{OF} = \cos A 	imes \sin B$.

Thus, the expression simplifies, leading to the relationship that includes $\cos A$ in Line 5.

Explain why $\frac{PF}{EF} \times \frac{EF}{OF}$ in Line 4 leads to $\cos A$ in Line 5 - AQA - A-Level Maths Pure - Question 14 - 2018 - Paper 1

Worked Solution & Example Answer:Explain why $\frac{PF}{EF} \times \frac{EF}{OF}$ in Line 4 leads to $\cos A$ in Line 5 - AQA - A-Level Maths Pure - Question 14 - 2018 - Paper 1

Explain why PF/EF × EF/OF in Line 4 leads to cos A in Line 5

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