1-cos-81-cos3 -81-cos5 -81-cos7 -8-

The correct option is C [ 1+cosπ/8 ] [ 1+cos3π/8 ] [ 1+cos5π/8 ] [ 1+cos7π/8 ]= ( 1+cosπ/8 ) ( 1+cos3π/8 ) ( 1 cos3π/8 ) ( 1 cosπ/8 ) =( 1 cos^2π/8 ) ( 1 cos^ ...

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Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios of Compound Angles

1+cosπ/81+cos...

Question

$(1 + c o s \frac{π}{8}) (1 + c o s \frac{3 π}{8}) (1 + c o s \frac{5 π}{8}) (1 + c o s \frac{7 π}{8})$ =

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Solution

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

Suggest Corrections

(1+cosπ8)(1+cos3π8)(1+cos5π8)(1+cos7π8)=

The correct option is C [1+cosπ8][1+cos3π8][1+cos5π8][1+cos7π8]=(1+cosπ8)(1+cos3π8)(1−cos3π8)(1−cosπ8) =(1−cos2π8)(1−cos23π8)=sin2π8sin23π8)=(1−cosπ42)(1−cos3π42)=18

$(1 + c o s \frac{π}{8}) (1 + c o s \frac{3 π}{8}) (1 + c o s \frac{5 π}{8}) (1 + c o s \frac{7 π}{8})$ =