Match the following
In a triangle ABC,
Column-I Column-II
(a) $b cos C + c cos B$ (p) a
(b) $b^{2} + c^{2} - 2 b c cos A$ (q) $(a + b + c) a$
(c) $b c sin A$ (r) $a^{2}$
(d) $b sin A - a sin B$ (s) 0

(a) - (p),

(b) - (r),

(c) - (q),

(d) - (s)

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(a) - (q),

(b) - (r),

(c) - (p),

(d) - (s)

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(a) - (r),

(b) - (q),

(c) - (q),

(d) - (s)

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None of these

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Solution

The correct option is A $(a) - (p),$ $(b) - (r),$ $(c) - (q),$ $(d) - (s)$
(a) $∵ a = b cos C + c cos B$ ...(p)

(b) $∵ cos A = \frac{b + c - a}{2 b c}$ ...(r)

(c) $sin A = \frac{(a + b + c) a}{b c}$

$∴ b c sin A = (a + b + c) a$ ......(q)

(d) $b sin A - a sin B = 0$ ...(s)

as $\frac{a}{sin A} = \frac{b}{sin B}$

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	Column-I		Column-II
(a)	$b cos C + c cos B$	(p)	a
(b)	$b^{2} + c^{2} - 2 b c cos A$	(q)	$(a + b + c) a$
(c)	$b c sin A$	(r)	$a^{2}$
(d)	$b sin A - a sin B$	(s)	0

Match the following In a triangle ABC,Column-IColumn-II(a)bcosC+ccosB(p)a(b)b2+c2−2bccosA(q)(a+b+c)a(c)bcsinA(r)a2(d)bsinA−asinB(s)0

The correct option is A (a)−(p),(b)−(r),(c)−(q),(d)−(s)(a) ∵a=bcosC+ccosB ...(p)(b) ∵cosA=b+c−a2bc ...(r)(c) sinA=(a+b+c)abc∴bcsinA=(a+b+c)a......(q)(d) bsinA−asinB=0 ...(s)as asinA=bsinB

Match the following
In a triangle ABC,
Column-I Column-II
(a) $b cos C + c cos B$ (p) a
(b) $b^{2} + c^{2} - 2 b c cos A$ (q) $(a + b + c) a$
(c) $b c sin A$ (r) $a^{2}$
(d) $b sin A - a sin B$ (s) 0