If $$cos x + cos^{2} x = 1,$$ then $$sin^{8} x + 2 sin^{6} x + sin^{4}$$ x is equal to
$$cos x + cos^2 x = 1$$
=> $$cos x = 1 - cos^2 x$$
=> $$cos x = sin^2 x$$
$$\therefore$$ $$sin^{8} x + 2 sin^{6} x + sin^{4} x$$
= $$(sin^4 x + sin^2 x)^2$$
= $$((cos x)^2 + sin^2 x)^2$$
= $$(cos^2 x + sin^2 x)^2 = 1$$
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