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Differentiate. (cos 3x-cosx)/(cos5x-cos3...

Differentiate.
`(cos 3x-cosx)/(cos5x-cos3x)`

Text Solution

Verified by Experts

`y=(cos3x-cosx)/(cos5x-cos3x)=(-2sin2xcdot sinx)/(-2sin4xcdot sin2x)`
`=(sin2x)/(sin4x)=1/(2cos2x)`
`=1/2sec2x`
`thereforedy/dx=1/2sec2xcdottan2xcdot2`
`=sec2x tan 2x`
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