In triangle ABC given 9 a 2-9 b 2-17 c 2If A- B - C - m - n then the value of m - n equalsB- 5C- 7D- 9

The correct option is A 13A=cos Asin A=(b^2+c^2 a^2)Rabc B=cos Bsin B=(a^2+c^2 b^2)Rabc C=cos Csin C=(b^2+a^2 c^2)Rabc A+ B C=a^2+b^2+2c^2 a^2 b^2b^2+a^2 c^2 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Area Using Sine Rule

In triangle A...

Question

In triangle $A B C$ given $9 a^{2} + 9 b^{2} = 17 c^{2}$
If $\frac{cot A + cot B}{cot C} = \frac{m}{n}$ then the value of $(m + n)$ equals

13

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

5

No worries! We‘ve got your back. Try BYJU‘S free classes today!

7

No worries! We‘ve got your back. Try BYJU‘S free classes today!

9

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $13$
$cot A = \frac{cos A}{sin A} = \frac{(b^{2} + c^{2} - a^{2}) R}{a b c}$
$cot B = \frac{cos B}{sin B} = \frac{(a^{2} + c^{2} - b^{2}) R}{a b c}$
$cot C = \frac{cos C}{sin C} = \frac{(b^{2} + a^{2} - c^{2}) R}{a b c}$
$\frac{cot A + cot B}{cot C} = \frac{a^{2} + b^{2} + 2 c^{2} - a^{2} - b^{2}}{b^{2} + a^{2} - c^{2}} = \frac{2 c^{2}}{\frac{17}{9} c^{2} - c^{2}} = \frac{9}{4}$

Suggest Corrections

Similar questions

Q. If

l, m, n

denote the sides of pedal triangle opposite to the vertices

A, B, C

respectively of triangle

A B C .

Then the value of

\frac{l}{a^{2}} + \frac{m}{b^{2}} + \frac{n}{c^{2}}

is :

Find the perimeter of a triangle whose sides are 8n + 5m, - 3n - 4m and 4n + 4m.

In triangle ABC, AB=m²-n², BC=2mn and AC=m²+n², the value of angle ABC is-

A)90°

B)30°

C)60°

D)45°

Q. If

5 {log}_{a b c} (a^{3} + b^{3} + c^{3}) = 3 λ (\frac{1 + {log}_{3} (a b c)}{{log}_{3} a b c})

and

{(a b c)}^{a + b + c} = 1

and

λ = \frac{m}{n}

, where

m

and

n

are relatively prime, then the value of

| m + n | + | m - n | =

Q. Assertion :In a triangle

A B C, \frac{a^{2} + b^{2} + c^{2}}{△} \geq 4 \sqrt{3}

Reason: If

a_{i} > 0, i = 1, 2, 3, . . ., n

which are not identical, then

\frac{a_{1}^{m} + a_{2}^{m} + . . . + a_{n}^{m}}{n} > {(\frac{a_{1} + a_{2} + . . . + a_{n}}{n})}^{m},

m < 0

m > 1

Join BYJU'S Learning Program

In triangle ABC given 9a2+9b2=17c2 If cotA+cotBcotC=mn then the value of (m+n) equals

The correct option is A 13cotA=cosAsinA=(b2+c2−a2)Rabc cotB=cosBsinB=(a2+c2−b2)Rabc cotC=cosCsinC=(b2+a2−c2)Rabc cotA+cotBcotC=a2+b2+2c2−a2−b2b2+a2−c2=2c2179c2−c2=94

In triangle $A B C$ given $9 a^{2} + 9 b^{2} = 17 c^{2}$
If $\frac{cot A + cot B}{cot C} = \frac{m}{n}$ then the value of $(m + n)$ equals