The value of sin-4- sin3-4- sin5-4 -sin7-4 is

The correct option is D 14 sinπ4·sin3π4·sin5π4·sin7π4 =sinπ4·sin (π π4 )· #160; sin (π +π4 )·sin (2π π4 ) =sinπ4·sinπ4 ( sinπ4 )· ( sin ...

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Standard XII

Mathematics

Sign of Trigonometric Ratios in Different Quadrants

The value of ...

Question

The value of $sin \frac{π}{4} . sin \frac{3 π}{4} . sin \frac{5 π}{4} . sin \frac{7 π}{4}$ is

\sqrt{\frac{2}{7}}

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\frac{1}{4}

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\frac{1}{8}

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1

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Solution

The correct option is D $\frac{1}{4}$
$sin \frac{π}{4} \cdot sin \frac{3 π}{4} \cdot sin \frac{5 π}{4} \cdot sin \frac{7 π}{4}$
$= sin \frac{π}{4} \cdot sin (π - \frac{π}{4}) \cdot sin (π + \frac{π}{4}) \cdot sin (2 π - \frac{π}{4})$
$= sin \frac{π}{4} \cdot sin \frac{π}{4} (- sin \frac{π}{4}) \cdot (- sin \frac{π}{4})$
$= \frac{1}{\sqrt{2}} \cdot \frac{1}{\sqrt{2}} \cdot \frac{- 1}{\sqrt{2}} \cdot \frac{- 1}{\sqrt{2}} = \frac{1}{4}$

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Similar questions

$c o s \frac{π}{7}$ . $c o s \frac{3 π}{7}$ . $c o s \frac{5 π}{7}$ are the roots of the equation $8 x^{3} - 4 x^{2} - 4 x + 1 = 0$ . Then the value of $s i n \frac{π}{14} . s i n \frac{3 π}{14} . s i n \frac{5 π}{14}$ is

Match the column

$\begin{matrix} Column A & Column B 1.cos \frac{2 π}{7} + cos \frac{4 π}{7} + cos \frac{6 π}{7} & A.0 2.cos \frac{π}{7} + cos \frac{2 π}{7} +cos \frac{3 π}{7} + cos \frac{4 π}{7} + cos \frac{5 π}{7} + cos \frac{6 π}{7} & B. \frac{1}{2} 3.sin \frac{π}{11} + sin \frac{3 π}{11} + sin \frac{5 π}{11} + sin \frac{7 π}{11} + sin \frac{9 π}{11} & C. \frac{- 1}{2} \end{matrix}$

Q. Find the value of

sin \frac{π}{14} . sin \frac{3 π}{14} . sin \frac{5 π}{14} . sin \frac{7 π}{14} sin \frac{9 π}{14} sin \frac{11 π}{14} . sin \frac{13 π}{14}

Q. The value of

sin \frac{π}{14} \cdot sin \frac{3 π}{14} \cdot sin \frac{5 π}{14} \cdot sin \frac{7 π}{14} \cdot sin \frac{9 π}{14} \cdot sin \frac{11 π}{14} \cdot sin \frac{13 π}{14}

is equal to

Q. Assertion :Numerical value of expression

x = 4 {log}_{5} 2 + {log}_{5} sin \frac{π}{5} + {log}_{5} sin \frac{2 π}{5} + {log}_{5} sin \frac{3 π}{5} + {log}_{5} sin \frac{4 π}{5}

1

. Reason:

sin 18^{o} = \frac{1}{4} (\sqrt{5} - 1)

and

cos 36^{o} = \frac{1}{4} (\sqrt{5} + 1)

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The value of sinπ4.sin3π4.sin5π4.sin7π4 is

The correct option is D 14sinπ4⋅sin3π4⋅sin5π4⋅sin7π4=sinπ4⋅sin(π−π4)⋅sin(π+π4)⋅sin(2π−π4)=sinπ4⋅sinπ4(−sinπ4)⋅(−sinπ4)=1√2⋅1√2⋅−1√2⋅−1√2=14

The value of $sin \frac{π}{4} . sin \frac{3 π}{4} . sin \frac{5 π}{4} . sin \frac{7 π}{4}$ is