જો frac{x}{cos alpha} = frac{y}{cos left(frac | vedclass

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(B) ધારો કે $\frac{x}{\cos \alpha} = \frac{y}{\cos \left(\frac{2 \pi}{3} - \alpha\right)} = \frac{z}{\cos \left(\frac{2 \pi}{3} + \alpha\right)} = k$.

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(B) ધારો કે $\frac{x}{\cos \alpha} = \frac{y}{\cos \left(\frac{2 \pi}{3} - \alpha\right)} = \frac{z}{\cos \left(\frac{2 \pi}{3} + \alpha\right)} = k$. તેથી,$x = k \cos \alpha$,$y = k \cos \left(\frac{2 \pi}{3} - \alpha\right)$,અને $z = k \cos \left(\frac{2 \pi}{3} + \alpha\right)$. હવે,$x + y + z = k \left[ \cos \alpha + \cos \left(\frac{2 \pi}{3} - \alpha\right) + \cos \left(\frac{2 \pi}{3} + \alpha\right) \right]$. સૂત્ર $\cos(A - B) + \cos(A + B) = 2 \cos A \cos B$ નો ઉપયોગ કરતા: $x + y + z = k \left[ \cos \alpha + 2 \cos \left(\frac{2 \pi}{3}\right) \cos \alpha \right]$. કારણ કે $\cos \left(\frac{2 \pi}{3}\right) = -\frac{1}{2}$,તેથી: $x + y + z = k \left[ \cos \alpha + 2 \left(-\frac{1}{2}\right) \cos \alpha \right] = k [\cos \alpha - \cos \alpha] = 0$.

જો $\frac{x}{\cos \alpha} = \frac{y}{\cos \left(\frac{2 \pi}{3} - \alpha\right)} = \frac{z}{\cos \left(\frac{2 \pi}{3} + \alpha\right)}$ હોય,તો $(x + y + z)$ ની કિંમત કેટલી થાય?

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