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If in ABC, a B C + b C A+ c A B= {m}{R}.Find m

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If in $△ A BC$ , $a cos B cos C + b cos C cos A + c cos A cos B = \frac{m △}{R}$ .Find $m$

A

1

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If in

△ A BC

,

a cos B cos C + b cos C cos A + c cos A cos B = \frac{m △}{R}

.Find

m

10 mins ago

Discuss this question LIVE

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Text solutionVerified

ABC is a triangle.

\frac{sin A}{a} = \frac{sin B}{b} = \frac{sin C}{c} = \frac{1}{2 R}

-------1

\Rightarrow △ = 2 R^{2} sin A sin B sin C

\Rightarrow \frac{m △}{R} = 2 R m sin A sin B sin C

Given,

a cos B cos C + b cos A cos C + c cos A cos B = \frac{m △}{R}

\Rightarrow cos B (a cos C + c cos A) + b cos A cos C = \frac{m △}{R}

\Rightarrow b cos B + b cos A cos C = \frac{m △}{R}

( As

b = a cos C + c cos A

).

\Rightarrow b (- cos (A + C) + cos A cos C) = \frac{m △}{R}

( As

A + C = π - B

)

\Rightarrow b sin A sin C = \frac{m △}{R}

\Rightarrow 2 R sin A sin B sin C = \frac{m △}{R}

(As

b = 2 R sin B

)

\Rightarrow 2 R sin A sin B sin C = 2 R m sin A sin B sin C

∴ m = 1

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Question Text	If in $△ A BC$ , $a cos B cos C + b cos C cos A + c cos A cos B = \frac{m △}{R}$ .Find $m$
Answer Type	Text solution:1
Upvotes	150