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sin(pi/10)sin((3pi)/10)...

`sin(pi/10)sin((3pi)/10)`

A

`(1)/(2)`

B

`-(1)/(2)`

C

`-(1)/(4)`

D

1

Text Solution

Verified by Experts

Given expression, `sin""(pi)/(10)sin""(13pi)/(10)` =`sin""(pi)/(10)sin(pi+(3pi)/(10))`
`" "= -sin""(pi)/(10)sin""(3pi)/(10)=-sin18^(@)*sin54^(@)`
`" "=-sin18^(@)*cos36^(@)`
`" "=-((sqrt(5)-1)/(4))((sqrt(5)+1)/(4))" "` [since, put this value here]
`" " =-((5-1)/(16))=-(1)/(4)`
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