Question

(cos x\2 - sin x\2)^2 нужно скорее

Answer 1

Ответ:

${( \cos( \frac{x}{2} ) - \sin( \frac{x}{2} ) )}^{2} = \\ = \cos {}^{2} ( \frac{x}{2} ) - 2 \sin( \frac{x}{2} ) \cos( \frac{x}{2} ) + \sin {}^{2} ( \frac{x}{2} ) = \\ - - - - - - - - - - - - - \\ \cos {}^{2} ( \frac{x}{2} ) + \sin {}^{2} ( \frac{x}{2} ) = 1 \\ 2\cos( \frac{x}{2} ) \sin( \frac{x}{2} ) = \sin(x) \\ - - - - - - - - - - - - - - \\ = 1 - \sin(x)$