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

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

A

`sin 7^(@)`

B

`cos 7^(@)`

C

`sin 36^(@)`

D

`cos 36^(@)`

Text Solution

Verified by Experts

The correct Answer is:
B
`sin47^(@)-sin25^(@)+sin61^(@)-sin11^(@)`
`=2cos36^(@)sin11^(@)+2cos36^(@)sin25^(@)`
`=2cos36^(@)[sin11^(@)+sin25^(@)]`
`=2cos36^(@)[2sin((25^(@)+11^(@))/(2))cos((25^(@)-11^(@))/(2))]`
`=4((sqrt(5)+1)/(4))((sqrt(5)-1)/(4))cos7^(@)=(5-1)/(4)cos7^(@)`
`=cos7^(@)`
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