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lim(x→0)[1/(sinx)^2-(cosx)^2/x^2]

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lim(x→0)[1/(sinx)^2-(cosx)^2/x^2]
lim(x→0)[1/(sinx)^2-(cosx)^2/x^2]
=lim(x→0)[x^2-sin^2 x(cosx)^2]/[x^2(sinx)^2]
=lim(x→0)[x^2-sin^2 x(cosx)^2]/[x^4]
=lim(x→0)[x^2-1/4sin^2 (2x)]/[x^4] (0/0)
=lim(x→0)[2x-sin (2x)cos(2x)]/[4x^3]
=lim(x→0)[2x-1/2sin (4x)]/[4x^3] (0/0)
=lim(x→0)[2-2cos (4x)]/[12x^2]
=lim(x→0)(4x)^2/[12x^2]
=4/3