The value ofsin -14sin 3-14sin 5-14sin 7-14sin 9-14sin 11-14sin 13-14 is equal to

Sin π/14sin 3π/14sin 5π/14sin 7π/14sin 9π/14sin 11π/14sin 13π/14 = ( sin π/14sin 3π/14sin 5π/14 )^2 = [cos (π/2 π/14 ) cos (π/2 3π/14 )cos (π/2 5π/14 ) ]^ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios of Allied Angles

The value ofs...

Question

The value of
$s i n \frac{π}{14} s i n \frac{3 π}{14} s i n \frac{5 π}{14} s i n \frac{7 π}{14} s i n \frac{9 π}{14} s i n \frac{11 π}{14} s i n \frac{13 π}{14}$ is equal to ___

\frac{1}{64}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{1}{32}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{1}{16}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{1}{8}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{1}{64}$
$s i n \frac{π}{14} s i n \frac{3 π}{14} s i n \frac{5 π}{14} s i n \frac{7 π}{14} s i n \frac{9 π}{14} s i n \frac{11 π}{14} s i n \frac{13 π}{14} = {(s i n \frac{π}{14} s i n \frac{3 π}{14} s i n \frac{5 π}{14})}^{2} = {[c o s (\frac{π}{2} - \frac{π}{14}) c o s (\frac{π}{2} - \frac{3 π}{14}) c o s (\frac{π}{2} - \frac{5 π}{14})]}^{2} = {[c o s \frac{3 π}{7} c o s \frac{2 π}{7} c o s \frac{π}{7}]}^{2} = {[c o s \frac{π}{7} c o s \frac{2 π}{7} c o s \frac{4 π}{7}]}^{2} = {(\frac{1}{8 s i n \frac{π}{7}} s i n \frac{8 π}{7})}^{2} = {(\frac{s i n (π + \frac{π}{7})}{8 s i n \frac{π}{7}})}^{2} = {(\frac{- s i n \frac{π}{7}}{8 s i n \frac{π}{7}})}^{2} = {(\frac{1}{8})}^{2} = \frac{1}{64}$

Suggest Corrections

Similar questions

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}

is equal to

Q. 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}

is equal to

Q. If

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} = \frac{1}{k},

then

k

is equal to

Solve

Sin π/14 sin 3π/14 sin 5π/14 sin 7π/14 sin 9π/14 sin 11π/14 sin 13π/14 sin 13π/14 = ? ( Also Name the trigonometric functions used)

Q. If 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}

is equal to

k^{2}

, then

k^{2}

is equal to

Join BYJU'S Learning Program

The value of sinπ14sin3π14sin5π14sin7π14sin9π14sin11π14sin13π14 is equal to ___

The correct option is A 164sinπ14sin3π14sin5π14sin7π14sin9π14sin11π14sin13π14=(sinπ14sin3π14sin5π14)2=[cos(π2−π14)cos(π2−3π14)cos(π2−5π14)]2=[cos3π7cos2π7cosπ7]2=[cosπ7cos2π7cos4π7]2=(18sinπ7sin8π7)2=(sin(π+π7)8sinπ7)2=(−sinπ78sinπ7)2=(18)2=164

The value of
$s i n \frac{π}{14} s i n \frac{3 π}{14} s i n \frac{5 π}{14} s i n \frac{7 π}{14} s i n \frac{9 π}{14} s i n \frac{11 π}{14} s i n \frac{13 π}{14}$ is equal to ___