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The value of (cos^4 1^@+cos^4 2^@+....+c...

The value of `(cos^4 1^@+cos^4 2^@+....+cos^4 179^@)-(sin^4 1^@+sin^4 2^@+.....+sin^4 179^@)` equals

Text Solution

Verified by Experts

The correct Answer is:
`-1`
`sumcos^(4)1^(@)-sumsin^(4)1^(@)`
`=sum(cos^(4)1^(@)-sin^(4)1^(@))`
`=sum cos2^(@)`
`=cos2^(@)+cos4^(@)+cos6^(@)+...........+cos 358^(@)`
`=(cos((2^(@)+358^(@))/(2))sin(179^(@)xx1^(@)))/(sin1^(@))`
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