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Sign of Trigonometric Ratios in Different Quadrants

The value of ...

Question

The value of $cot \frac{π}{20} cot \frac{3 π}{20} cot \frac{5 π}{20} cot \frac{7 π}{20} cot \frac{9 π}{20}$ is

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Solution

Given
$cot \frac{π}{20} cot \frac{3 π}{20} cot \frac{5 π}{20} cot \frac{7 π}{20} cot \frac{9 π}{20} = (cot \frac{π}{20} cot \frac{9 π}{20}) cot \frac{π}{4} (cot \frac{3 π}{20} cot \frac{7 π}{20}) = [cot \frac{π}{20} cot (\frac{π}{2} - \frac{π}{20})] [cot \frac{3 π}{20} cot (\frac{π}{2} - \frac{3 π}{20})] = (cot \frac{π}{20} tan \frac{π}{20}) (cot \frac{3 π}{20} tan \frac{3 π}{20}) = 1$

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cot \frac{π}{20} cot \frac{3 π}{20} cot \frac{5 π}{20} cot \frac{7 π}{20} cot \frac{9 π}{20} cot \frac{15 π}{20} =

cot \frac{π}{20} cot \frac{3 π}{20} cot \frac{5 π}{20} cot \frac{7 π}{20} cot \frac{9 π}{20}

Q. Find the value of the trigonometric expression

cot (\frac{π}{20}) cot (\frac{3 π}{20}) cot (\frac{5 π}{20}) cot (\frac{7 π}{20}) cot (\frac{9 π}{20})

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cot \frac{π}{20} cot \frac{3 π}{20} cot \frac{7 π}{20} cot \frac{9 π}{20} cot \frac{15 π}{20} =

f (x) = \begin{matrix} \frac{k cos x}{π - 2 x} & w h e n x \neq \frac{π}{2} 3 & x = \frac{π}{2} \end{matrix}

lim x \to \frac{π}{2} f (x) = f (\frac{π}{2})

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find the value of`k.

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Sign of Trigonometric Ratios in Different Quadrants

Standard XII Mathematics

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