lim x-->0 (cos 3x-cos 5x)/x^{2}

By using

cosC - cosD = -2 (sin(C+D)/2) (sin(C-D)/2 )

Lt x -->0 {-2 sin 4x -sin x} / x^{2}

Lt x -->0 {2 sin 4x sin x) / v

Lt x -->0 { 2 (sin 4x )/4x (sin x)x } * 4x * x / x^{2}

Ans = 8

lim x-->0 (cos 3x-cos 5x)/x^{2}

By using

cosC - cosD = -2 (sin(C+D)/2) (sin(C-D)/2 )

Lt x -->0 {-2 sin 4x -sin x} / x^{2}

Lt x -->0 {2 sin 4x sin x) / v

Lt x -->0 { 2 (sin 4x )/4x (sin x)x } * 4x * x / x^{2}

Ans = 8

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