You can put this solution on YOUR website! Please prove this using Trigonometric Identities:
sin⁴x - cos⁴x + cos²x = sin²x
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starting with left side:
sin⁴x - cos⁴x + cos²x
difference of squares
(sin^2x+cos2^x)(sin^2x-cos^2x)+cos^2x
sin^2x=1-cos^2x
(1-cos^2x+cos^2x)(1-cos^2x-cos^2x)+cos^2x
(1)(1-2cos^2x)+cos^2x
1-2cos^2x+cos^2x
1-cos^2x=sin^2x
left side=right side
Identity verified
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