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sin47^@+sin61^@-sin11^@-sin25^@=...

`sin47^@+sin61^@-sin11^@-sin25^@=`

Text Solution

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`sin 47^(@)+sin61^(@)-sin11^(@)-sin^(@)`
`=(sin 47^(@)-sin25^(@))+(sin61^(@)-sin11^(@))`
`=2sin11^(@)cos36^(@)+2sin25^(@)cos36^(@)`
`=2cos 36^(@)(sin11^(@)+sin25^(@))`
`=2cos36^(@)(2sin18^(@)cos7^(@))`
`=4xx(sqrt(5)+1)/(4)xx(sqrt(5)-1)/(4)xxcos7^(@)`
`=cos 7^(@)`.
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