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[TEX]sin^8x + cos^8x = \frac{17}{18}cos^2{2x}[/TEX]
[TEX]\leftrightarrow (sin^4x + cos^4x)^2 - 2sin^4x.cos^4x = \frac{17}{18}cos^2{2x}[/TEX]
[TEX]\leftrightarrow [(sin^2x + cos^2x)^2 - 2sin^2x.cos^2x]^2 - 2sin^4x.cos^4x = \frac{17}{18}cos^2{2x} [/TEX]
[TEX]\leftrightarrow (1 - 2sin^2x.cos^2x)^2 - 2sin^4x.cos^4x = \frac{17}{18}cos^2{2x}[/TEX]
[TEX]\leftrightarrow 1 + 4sin^4x.cos^4x - 4sin^2x.cos^2x - 2sin^4x.cos^4x = \frac{17}{18}cos^2{2x}[/TEX]
[TEX]\leftrightarrow 1 + 2sin^4x.cos^4x - 4sin^2x.cos^2x = \frac{17}{18}(1 - sin^2{2x}) [/TEX]
[TEX]\leftrightarrow 1 + 2sin^4x.cos^4x - 4sin^2x.cos^2x - \frac{17}{18} + \frac{17}{18}sin^2{2x} = 0 [/TEX]
[TEX]\leftrightarrow \frac{1}{8}sin^4{2x} - \frac{1}{18}sin^2{2x} + \frac{1}{18} = 0[/TEX]
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