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Standard X

Mathematics

Trigonometric Ratio(sec,cosec,cot)

What is the v...

Question

What is the value of cot B in terms of a,b,c?

$\frac{b}{a}$

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$\frac{a}{b}$

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$\frac{c}{b}$

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$\frac{b}{c}$

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Solution

The correct option is B
$\frac{a}{b}$

We know that
$c o t B = \frac{Adjacent side}{Opposite Side}$

For the angle at B, the opposite side is AC and its length is $b$ . The adjacent side is BC, and its length is $a$ .

$∴ c o t B = \frac{B C}{A C} = \frac{a}{b}$

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Similar questions

Q. If a, b, c are real numbers such that

|\begin{matrix} b + c & c + a & a + b \\ c + a & a + b & b + c \\ a + b & b + c & c + a \end{matrix}| = 0

, then show that either

a + b + c = 0 or, a = b = c

Q. If

a, b

and

c

are real numbers and

Δ = ∣ ∣ ∣ ∣ \begin{matrix} b + c & c + a & a + b c + a & a + b & b + c a + b & b + c & c + a \end{matrix} ∣ ∣ ∣ ∣ = 0

,
show that either

a + b + c = 0

a = b = c

The determinant
$∣ ∣ ∣ ∣ ∣ \begin{matrix} b^{2} - a b & b - c & b c - a c a b - a^{2} & a - b & b^{2} - a b b c - a c & c - a & a b - a^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣$ equals to:

(a) abc(b-c)(c-a)(a-b)
(b) (b-c)(c-a)(a-b)
(c) (a+b+c)(b-c)(c-a)(a-b)
(d) None of these

Q. Prove the following identity:

\frac{a {(b - c)}^{2}}{(c - a) (a - b)} + \frac{b {(c - a)}^{2}}{(a - b) (b - c)} + \frac{c {(a - b)}^{2}}{(b - c) (c - a)} = a + b + c

Q. If

∣ ∣ ∣ ∣ \begin{matrix} b + c & c + a & a + b a + b & b + c & c + a c + a & a + b & b + c \end{matrix} ∣ ∣ ∣ ∣ = k ∣ ∣ ∣ ∣ \begin{matrix} a & b & c c & a & b b & c & a \end{matrix} ∣ ∣ ∣ ∣

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What is the value of cot B in terms of a,b,c?

The correct option is B ab We know that cot B=Adjacent side Opposite Side For the angle at B, the opposite side is AC and its length is b. The adjacent side is BC, and its length is a. ∴cot B=BCAC=ab

The correct option is B
$\frac{a}{b}$

We know that
$c o t B = \frac{Adjacent side}{Opposite Side}$

For the angle at B, the opposite side is AC and its length is $b$ . The adjacent side is BC, and its length is $a$ .

$∴ c o t B = \frac{B C}{A C} = \frac{a}{b}$