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Answer:
1/8
Step-by-step explanation:
cos pi/7 × cos 2pi/7 × cos 3pi/7
"now , we now sin2a = 2sinacosa"
multiply and divide by 2sin pi/7
1/2sin pi/7 { 2sin pi/7 cos pi/7 × cos 2pi/7 × cos 3pi/7 }
1/2sin pi/7 { sin 2pi/7 cos 2pi/7 × cos 3pi/7 }
"now , multiply and divide by 2"
1/2×2sin pi/7 { 2sin 2pi/7 cos 2pi/7 × cos 3pi/7 }
1/4sin pi/7 { sin 4pi/7 × cos 3pi/7 }
"as we now sin ( pi - theta ) = sin theta "
'sin ( pi - 4pi/7 ) = sin 3pi/7' , substitute this value,,,
1/4sin pi/7 { sin 3pi/7 cos 3pi/7 }
" again multiply and divide by 2 "
1/2×4sin pi/7 { 2sin 3pi/7 cos 3pi/7 }
1/8sin pi/7 { sin 6pi/7 }
" we can write sin 6pi/7 as sin ( pi - pi/7 ) and the value of sin ( pi - pi/7 ) = sin pi/7 ,,, substitute it "
NOW,,
sin pi/7/8sin pi/7
= 1/8
hope u understood
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