22(sin^2 72-cos^2 72)/cos144

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To simplify this expression, we first expand and simplify the numerator
sin^2 72 - cos^2 72 = (sin 72)(sin 72) - (cos 72)(cos 72
= sin^2 72 - cos^2 7
= sin^2 72 - (1 - sin^2 72) [using the Pythagorean identity sin^2 x + cos^2 x = 1
= 2sin^2 72 - 1

Therefore, the expression becomes
= [2sin^2 72 - 1]/cos 144

Now, since sin (180 - x) = sin x, we have sin 144 = sin (180 - 36) = sin 3
Also, cos (180 - x) = -cos x, we have cos 144 = -cos 36

So, the expression becomes
= [2sin^2 72 - 1]/(-cos 36
= [2(sin^2 72 - cos^2 72) - 1]/(-cos 36
= [2(2sin^2 36 - 1) - 1]/(-cos 36
= [4sin^2 36 - 2 - 1]/(-cos 36
= [4(sin^2 36) - 3]/(-cos 36
= [4(1 - cos^2 36) - 3]/(-cos 36
= [4 - 4cos^2 36 - 3]/(-cos 36
= [1 - 4cos^2 36]/(-cos 36
= [1 - 4cos^2 36]/(-cos 36)

Therefore, the simplified expression is [1 - 4cos^2 36]/(-cos 36).