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The value of (sin22^(@)cos8^(@)+cos158^(...

The value of `(sin22^(@)cos8^(@)+cos158^(@)cos98^(@))/(sin23^(@)cos7^(@)+cos157^(@)cos97^(@))`

A

1

B

2

C

`1/2`

D

`1/4`

Text Solution

Verified by Experts

The correct Answer is:
A
`(sin 22^(@)cos 8^(@)+cos158^(@)cos 98^(@))/(sin 23^(@)cos 7^(@)+cos 157^(@)cos 97^(@))`
`=(sin 22^(@)cos 8^(@)+cos(180^(@)-22^(@))cos (90^(@)+8^(@)))/(sin 23^(@)cos 7^(@)+cos(180^(@)-23^(@))cos(90^(@)+7^(@)))`
`=(sin 22^(2)cos 8^(@)+cos 22^(@)sin 8^(@))/(sin 23^(@)cos 7^(@)+cos 23^(@)sin 7^(@))`
`=(sin 30^(@))/(sin 30^(@))=1`
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