The trigonometric identity `sin^4x - cos^4x = 2*sin^2x - 1` has to be proved.
Start from the left hand side.
`sin^4x - cos^4x`
Use the relation `x^2 - y^2 = (x - y)(x +y)`
= `(sin^2x - cos^2x)(sin^2x + cos^2x)`
Use the property `sin^2x + cos^2x = 1`
= `(sin^2x...
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The trigonometric identity `sin^4x - cos^4x = 2*sin^2x - 1` has to be proved.
Start from the left hand side.
`sin^4x - cos^4x`
Use the relation `x^2 - y^2 = (x - y)(x +y)`
= `(sin^2x - cos^2x)(sin^2x + cos^2x)`
Use the property `sin^2x + cos^2x = 1`
= `(sin^2x - cos^2x)`
= `sin^2x - (1 - sin^2x)`
= `sin^2x - 1 + sin^2x`
= `2*sin^2x - 1`
This proves that `sin^4x - cos^4x = 2*sin^2x - 1`