Trigonometric Functions — MATHS STD 11 Science — Question

2. b² - c²

Solution:

Using cosine rule, we have

$\text{a(b}\cos\text{C}-\text{c}\cos\text{B})$

$=\text{ab}\Big(\frac{\text{a}^2+\text{b}^2-\text{c}^2}{2\text{ab}}\Big)-\text{ca}\Big(\frac{\text{c}^2+\text{a}^2-\text{b}^2}{2\text{ca}}\Big)$

$=\frac{\text{a}^2+\text{b}^2-\text{c}^2-\text{c}^2-\text{a}^2+\text{b}^2}{2}$

$=\frac{2\text{b}^2-2\text{c}^2}{2}$

$=\text{b}^2-\text{c}^2$

Hence, the correct answer is option (b).