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Evaluate Limit sin ( pi cos^2 (tan (sin x))) / x^2 As x-->0

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Solution: We have ,

$lim _x o 0fracsin (pi cos^2( an(sin x)))x^2$

$Rightarrow$ $=lim_x o0fracsin pi(1-sin^2 an (sin x))x^2$

$\ \ Rightarrow lim_x o0fracsin pi sin^2 an (sin x)pi sin^2 an (sin x) imes fracpi sin^2 an (sin x) an^2(sin x) imes frac an^2(sin x)sin^2x imes fracsin^2xx^2=pi$

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Deependra Verma

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