The value of cos pi/10 cos 2pi/10 cos 4pi/10 cos 8pi/10 cos16pi/10 is - Maths - Trigonometric Functions

Question

The value of cos pi/10 cos 2pi/10 cos 4pi/10 cos 8pi/10 cos16pi/10
is

Ishwarmani · Accepted Answer

Dear
Student,
Please find
below the solution to the asked query:

cosπ10cos2π10cos4π10cos8π10cos16π10Muliplying numerator and denominator by 2sinπ10, we get12sinπ10×2sinπ10cosπ10cos2π10cos4π10cos8π10cos16π10=12sinπ10×sin2π10cos2π10cos4π10cos8π10cos16π10         As, 2sinπ10cosπ10=sin2π10Muliplying numerator and denominator by 2, we get=14sinπ10×2sin2π10cos2π10cos4π10cos8π10cos16π10=14sinπ10×sin4π10cos4π10cos8π10cos16π10                          As, 2sin2π10cos2π10=sin4π10
=132sinπ10×sin32π10=sin3π+2π1032sinπ10=-sin2π1032sinπ10                                        As, sin3π+θ=-sinθ=-2sinπ10cosπ1032sinπ10                     As, sin2π10=2sinπ10cosπ10=-116cosπ10

Hope
this
information will clear
your doubts about the
topic

If you have
any more doubts just ask here on the forum and our experts
will
try to help
you out as soon as possible
Regards