Find the value of the trigonometric expression -20 3 -20 5 -20 7 -20 9 -20 -

The correct option is C ( π/20 ) × ( 9π/20 ) × ( 5π/20 ) × ( 3π/20 ) × ( 7π/20 ) = ( π/20 ) × ( π/2 π/20 ) × ( π/4 ) × ( 3π/20 ) × ( π/2 3π/20 ) = ( π/20 ...

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Byju's Answer

Standard X

Mathematics

Standard Values of Trigonometric Ratios

Find the valu...

Question

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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Solution

The correct option is D
$cot (\frac{π}{20}) \times cot (\frac{9 π}{20}) \times cot (\frac{5 π}{20}) \times cot (\frac{3 π}{20}) \times cot (\frac{7 π}{20})$
$= cot (\frac{π}{20}) \times cot (\frac{π}{2} - \frac{π}{20}) \times cot (\frac{π}{4}) \times cot (\frac{3 π}{20}) \times cot (\frac{π}{2} - \frac{3 π}{20})$
$= cot (\frac{π}{20}) \times tan (\frac{π}{20}) \times cot (\frac{π}{4}) \times cot (\frac{3 π}{20}) \times tan (\frac{3 π}{20})$
= $1$

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Similar questions

Q. 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}

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}

is equal to

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

Q. The trigonometric expression

{cot}^{2} 0 [\frac{sec θ - 1}{1 + sin θ}] + {sec}^{2} 0 [\frac{sin θ - 1}{1 + sec θ}]

has the value

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Find the value of the trigonometric expression cot(π20)cot(3π20)cot(5π20)cot(7π20)cot(9π20).

The correct option is D cot(π20)×cot(9π20)×cot(5π20)×cot(3π20)×cot(7π20) =cot(π20)×cot(π2−π20)×cot(π4)×cot(3π20)×cot(π2−3π20) =cot(π20)×tan(π20)×cot(π4)×cot(3π20)×tan(3π20) = 1

Find the value of the trigonometric expression
$cot (\frac{π}{20}) cot (\frac{3 π}{20}) cot (\frac{5 π}{20}) cot (\frac{7 π}{20}) cot (\frac{9 π}{20})$ .