cot frac{pi}{16} cdot cot frac{2 pi}{16} cdot | vedclass

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(B) ધારો કે $P = \cot \frac{\pi}{16} \cdot \cot \frac{2 \pi}{16} \cdot \cot \frac{3 \pi}{16} \cdot \cot \frac{4 \pi}{16} \cdot \cot \frac{5 \pi}{16} \

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$1$

Vedclass · Answer

(B) ધારો કે $P = \cot \frac{\pi}{16} \cdot \cot \frac{2 \pi}{16} \cdot \cot \frac{3 \pi}{16} \cdot \cot \frac{4 \pi}{16} \cdot \cot \frac{5 \pi}{16} \cdot \cot \frac{6 \pi}{16} \cdot \cot \frac{7 \pi}{16}$.ગુણધર્મ $\cot(\frac{\pi}{2} - 	heta) = 	an 	heta$ નો ઉપયોગ કરીને,આપણે છેલ્લા ત્રણ પદોને ફરીથી લખી શકીએ છીએ:$\cot \frac{5 \pi}{16} = 	an \frac{3 \pi}{16}$,$\cot \frac{6 \pi}{16} = 	an \frac{2 \pi}{16}$,$\cot \frac{7 \pi}{16} = 	an \frac{\pi}{16}$.આ કિંમતો મૂકતા:$P = (\cot \frac{\pi}{16} \cdot 	an \frac{\pi}{16}) \cdot (\cot \frac{2 \pi}{16} \cdot 	an \frac{2 \pi}{16}) \cdot (\cot \frac{3 \pi}{16} \cdot 	an \frac{3 \pi}{16}) \cdot \cot \frac{4 \pi}{16}$$\cot 	heta \cdot 	an 	heta = 1$ હોવાથી:$P = 1 \cdot 1 \cdot 1 \cdot \cot \frac{\pi}{4} = 1$.

$\cot \frac{\pi}{16} \cdot \cot \frac{2 \pi}{16} \cdot \cot \frac{3 \pi}{16} \cdot \cot \frac{4 \pi}{16} \cdot \cot \frac{5 \pi}{16} \cdot \cot \frac{6 \pi}{16} \cdot \cot \frac{7 \pi}{16} = $

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