prove 2sin^2 - 1 = sin^2 - cos ^2

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gsenviro | College Teacher | (Level 1) Educator Emeritus

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`2 sin^2x -1 = sin^2 x- cos^2 x`

Let us start with the left hand side of the equation.

Using the identity, `sin^2 x + cos^2 x = 1 `

we get: `2sin^2 x - 1 = 2sin^2x - (sin^2x + cos^2x) = 2sin^2 x - sin^2 x - cos^2x`

`= sin^2 x - cos^2 x`

which is the right hand side of the given question. Hence proved.