Prove the identity: `cos^2y +tan^2y - 1 = tan^2y*sin^2y`  

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We have to verify the identity: `cos^2 y + tan^2 y - 1 = tan^2 y * sin ^2 y`

`cos^2 y + tan^2 y - 1`

=> `cos^2 y + (sin^2 y)/(cos^2y) - 1`

=> `(1 - sin^2y) + (sin^2y)/(cos^2y) - 1`

=> `-sin^2y + (sin^2y)/(cos^2y)`

=> `(sin^2y)(1 - cos^y)/cos^y`

=> `sin^2y(sin^2y)/(cos^2y)`

=> `sin^2y*tan^2y`

This proves that `cos^2y + tan^2y - 1 = tan^2y*sin^2y`

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