In any triangle ABC,a(b cos C - c cos B) equa | vedclass

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(B) Using the projection formula or the cosine rule: $\cos C = \frac{a^2 + b^2 - c^2}{2ab}$ and $\cos B = \frac{a^2 + c^2 - b^2}{2ac}$.Substituting th

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$b^2 - c^2$

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(B) Using the projection formula or the cosine rule: $\cos C = \frac{a^2 + b^2 - c^2}{2ab}$ and $\cos B = \frac{a^2 + c^2 - b^2}{2ac}$.Substituting these into the expression:$a(b \cos C - c \cos B) = a(b \cdot \frac{a^2 + b^2 - c^2}{2ab} - c \cdot \frac{a^2 + c^2 - b^2}{2ac})$$= a(\frac{a^2 + b^2 - c^2}{2a} - \frac{a^2 + c^2 - b^2}{2a})$$= \frac{a^2 + b^2 - c^2 - (a^2 + c^2 - b^2)}{2}$$= \frac{a^2 + b^2 - c^2 - a^2 - c^2 + b^2}{2}$$= \frac{2b^2 - 2c^2}{2}$$= b^2 - c^2$.

Column-$I$	Column-$II$
$(A)$ Blue-green algae	$(I)$ Spirogyra
$(B)$ Unicellular algae	$(II)$ Nostoc
$(C)$ Filamentous algae	$(III)$ Volvox
$(D)$ Colonial algae	$(IV)$ Chlamydomonas

In any $\triangle ABC$,$a(b \cos C - c \cos B)$ equals

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Match the following columns:
Column-$I$ Column-$II$
$(A)$ Blue-green algae $(I)$ Spirogyra
$(B)$ Unicellular algae $(II)$ Nostoc
$(C)$ Filamentous algae $(III)$ Volvox
$(D)$ Colonial algae $(IV)$ Chlamydomonas

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