In - ABC- circum radius is 3 and inradius is 1-5 units- If the value of a 2 A - b 2 3 B - c 3 4 C is m - n where m and n are prime numbers then m - n -2 is

Here 2r= R ⇒Δ ABC is an equilateral ⇒ a=2R ( √(3)/2 )=√(3)R=3√(3) ∴m+n/2=13+3/2=8 ...

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Standard XII

Physics

Power Delivered and Heat Dissipated in a Circuit

In Δ ABC, cir...

Question

In $Δ A B C$ , circum radius is 3 and inradius is 1.5 units. If the value of a $c o t^{2} A + b^{2} c o t^{3} B + c^{3} c o t^{4} C$ is $m \sqrt{n}$ (where m and n are prime numbers) then $\frac{m + n}{2}$ is___

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Solution

Here $2 r = R \Rightarrow Δ A B C$ is an equilateral
$\Rightarrow a = 2 R (\frac{\sqrt{3}}{2}) = \sqrt{3} R = 3 \sqrt{3}$
$∴ \frac{m + n}{2} = \frac{13 + 3}{2} = 8$

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In ΔABC, circum radius is 3 and inradius is 1.5 units. If the value of a cot2A+b2cot3B+c3cot4C is m√n (where m and n are prime numbers) then m+n2 is___

Here 2r=R⇒ΔABC is an equilateral ⇒a=2R(√32)=√3R=3√3 ∴m+n2=13+32=8

In $Δ A B C$ , circum radius is 3 and inradius is 1.5 units. If the value of a $c o t^{2} A + b^{2} c o t^{3} B + c^{3} c o t^{4} C$ is $m \sqrt{n}$ (where m and n are prime numbers) then $\frac{m + n}{2}$ is___

Here $2 r = R \Rightarrow Δ A B C$ is an equilateral
$\Rightarrow a = 2 R (\frac{\sqrt{3}}{2}) = \sqrt{3} R = 3 \sqrt{3}$
$∴ \frac{m + n}{2} = \frac{13 + 3}{2} = 8$