If R denotes circum radius- then- in ABC - b 2- c 2-2 aR is equal toA- sin B-CB- cos B-CC- None of theseD- cos B-cos C

The correct option is A sin(B C) b^2 c^2/2aR=4R^2(sin^2 B sin^2 C)/4R^2sin A=sin(B+C) sin(B C)/sin A =sin(B C) ...

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Trigonometric Ratios of Multiples of an Angle

If R denotes ...

Question

If R denotes circum radius, then, in $△ A B C, \frac{b^{2} - c^{2}}{2 a R}$ is equal to

cos(B-C)

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sin(B-C)

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cos B - cos C

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None of these

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Solution

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R

Δ A B C

\frac{b^{2} - c^{2}}{2 a R}

\frac{a^{2} - b^{2}}{cos A + cos B} + \frac{b^{2} - c^{2}}{cos B + cos C} + \frac{c^{2} - a^{2}}{cos C + cos A} = 0

\frac{b^{2} - c^{2}}{cos B + cos C} + \frac{c^{2} - a^{2}}{cos C + cos A} + \frac{a^{2} - b^{2}}{cos A + cos B} = 0.

Δ

\frac{b^{2} - c^{2}}{2 a R}

△ A B C

cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c}

cos B = \frac{c^{2} + a^{2} - b^{2}}{2 c a}, cos C = \frac{a^{2} + b^{2} - c^{2}}{2 a b}

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