Mark the correct alternative in each of the following:

In any ∆ABC, $a (b \cos C - c \cos B) =$

(a) $a^{2}$ (b) $b^{2} - c^{2}$ (c) 0 (d) $b^{2} + c^{2}$

Open in App

Solution

Using cosine rule, we have

$a (b \cos C - c \cos B) = a b (\frac{a^{2} + b^{2} - c^{2}}{2 a b}) - c a (\frac{c^{2} + a^{2} - b^{2}}{2 c a}) = \frac{a^{2} + b^{2} - c^{2} - c^{2} - a^{2} + b^{2}}{2} = \frac{2 b^{2} - 2 c^{2}}{2} = b^{2} - c^{2}$

Hence, the correct answer is option (b).

Suggest Corrections

Similar questions

Mark the correct alternative in each of the following :

$I n a n y Δ A B C, a (b c o s C - c c o s B) =$

2 a c \sin (\frac{A - B + C}{2})

a^{2} + b^{2} - c^{2}

c^{2} + a^{2} - b^{2}

b^{2} - c^{2} - a^{2}

c^{2} - a^{2} - b^{2}

Δ A B C

a (b cos C - c cos B) = b^{2} - c^{2}

Mark the correct alternative in each of the following :

$I n a n y Δ A B C, 2 (b c c o s A + c a c o s B + a b c o s C) =$

a b c

a + b + c

a^{2} + b^{2} + c^{2}

\frac{1}{a^{2}} + \frac{1}{b^{2}} + \frac{1}{c^{2}}

Join BYJU'S Learning Program