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Prove that: sin^4 theta - cos^4 theta=...

Prove that:
`sin^4 theta - cos^4 theta= 1-2 cos^2 theta`.

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In the textbook the question is
Prove `sec^4 theta - cos^4 theta = 1-2 cos^2 theta`.]
LHS `= sin^4 theta - cos^4 theta`
` = (sin^2 theta)^2 - (cos^2theta)^2`
…[`a^2 - b^2 = (a+b)(a-b)`]
`=1(sin^2theta - cos^2 theta)` ...`(sin^2theta + cos^2theta = 1)`
`=sin^2 theta -cos^2theta`
`=1-cos^2theta - cos^2 theta` ...[`(therefore sin^2 theta +cos^2 theta=1)/(therefore sin^2 theta =cos^2 theta)]`
`= 1-2 cos^2 theta`
= RHS
`therefore` LHS = RHS
`therefore sin^4 theta - cos^4 theta = 1-2 cos^2 theta`.
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