$\int\limits_0^\pi {\left( {{{\sin }^2}\cfrac{x}{2} - {{\cos }^2}\cfrac{x}{2}} \right)dx}$
$\int\limits_0^\pi {\left( {{{\sin }^2}\cfrac{x}{2} - {{\cos }^2}\cfrac{x}{2}} \right)dx}$
Official Solution
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NCERT & Exemplar
: Let$\int\limits_0^\pi {\left( {{{\sin }^2}\cfrac{x}{2} - {{\cos }^2}\cfrac{x}{2}} \right)dx} = - \int\limits_0^\pi {\cos x} dx$
$= - \left[ {\sin x} \right]_0^\pi = - \left( {\sin \pi - \sin 0} \right) = - \left( {0 - 0} \right) = 0$
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