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 ...

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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

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Solution

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

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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