If `x=(sin^3P)/cos^2P,y=cos^3P/sin^2P" and " sinP+cosP=1/2` then find the value of x + y.

Explanation

`x+y=sin^3p/cos^2p+cos^3p/sin^2p`

`x+y=(sin^5p+cos^5p)/(sin^2pcos^2p)`

`sin^5p+cos^5p=(sinp+cosp)(sin^4p-sin^3pcosp+sin^2pcos^2p-sinpcos^3p+cos^4p)`

`=(sinp+cosp)((sin^4p+cos^4p)-sin-cosp(sin^2p+cos^2p+sin^2pcos^2p))`

`=(sinp+cosp)(1-sin^2pcos^2p-sinpcosp)`

`sinp+cosp=1/2`

`sin^2p+cos^2p+2sinpcosp=1/4`

`2sinpcosp=1/4-1`

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