Question

Simplify `2sin^2beta+4cos(alpha+beta)sinalphasinbeta+cos2(alpha+beta)`

Answer 1

`2sin^2beta+4cos(alpha+beta)sinalphasinbeta+cos2(alpha+beta)`
`2sin^2beta+4cos(alpha+beta)(2sinalphasinbeta+cos(alpha+beta))`
`2sin^2beta-1+2cos(alpha+beta)(2sinalphasinbeta+cosalphacosbeta)`
`-cos2beta+2cos(alpha+beta)cos(alpha-beta)`
`-cos2beta+cos(alpha+beta+alpha-beta)+cos(alpha+beta-alpha+beta)`
`-cos2beta+2cosalpha+cos2beta`
`cos2alpha`.