If in a triangle ABC,frac{2 cos A}{a} + frac{ | vedclass

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(D) Using the cosine rule,$\cos A = \frac{b^2+c^2-a^2}{2bc}$,$\cos B = \frac{a^2+c^2-b^2}{2ac}$,and $\cos C = \frac{a^2+b^2-c^2}{2ab}$.Substituting th

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$\frac{\pi}{2}$

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(D) Using the cosine rule,$\cos A = \frac{b^2+c^2-a^2}{2bc}$,$\cos B = \frac{a^2+c^2-b^2}{2ac}$,and $\cos C = \frac{a^2+b^2-c^2}{2ab}$.Substituting these into the given equation:$\frac{2(b^2+c^2-a^2)}{2abc} + \frac{a^2+c^2-b^2}{2abc} + \frac{2(a^2+b^2-c^2)}{2abc} = \frac{a^2+b^2}{abc}$Multiplying by $2abc$:$2(b^2+c^2-a^2) + (a^2+c^2-b^2) + 2(a^2+b^2-c^2) = 2(a^2+b^2)$$2b^2 + 2c^2 - 2a^2 + a^2 + c^2 - b^2 + 2a^2 + 2b^2 - 2c^2 = 2a^2 + 2b^2$$3b^2 + c^2 + a^2 = 2a^2 + 2b^2$$b^2 + c^2 = a^2$Since $b^2 + c^2 = a^2$,by the converse of the Pythagorean theorem,$\angle A = 90^{\circ}$ or $\frac{\pi}{2}$.

If in a triangle $ABC$,$\frac{2 \cos A}{a} + \frac{\cos B}{b} + \frac{2 \cos C}{c} = \frac{a}{bc} + \frac{b}{ca}$,then the value of the angle $A$ is:

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