Question

Даю 20 баллов, Помогите пожалуйста ​

Answer 1

Ответ:

$\frac{ {( \cos( \frac{\pi}{11} ) + \sin( \frac{\pi}{11} ) )}^{2} }{ \cos {}^{2} ( \frac{\pi}{4} - \frac{\pi}{11} ) } = \\ = \frac{ {( \cos( \frac{\pi}{11} ) + \sin( \frac{\pi}{11} ) )}^{2} }{ {( \cos( \frac{\pi}{4} ) \cos( \frac{\pi}{11} ) + \sin( \frac{\pi}{11} ) \sin( \frac{\pi}{4} ) )}^{2} } = \\ = \frac{{( \cos( \frac{\pi}{11} ) + \sin( \frac{\pi}{11} ) )}^{2}}{ {( \frac{ \sqrt{2} }{2} \cos( \frac{\pi}{11} ) + \frac{ \sqrt{2} }{2} \sin( \frac{\pi}{11} ) )}^{2} } = \\ = \frac{{( \cos( \frac{\pi}{11} ) + \sin( \frac{\pi}{11} ) )}^{2}}{ {( \frac{ \sqrt{2} }{2}( \cos( \frac{\pi}{11} ) + \sin( \frac{\pi}{11} ) ) )}^{2} } = \\ = \frac{{( \cos( \frac{\pi}{11} ) + \sin( \frac{\pi}{11} ) )}^{2}}{ {( \frac{1}{ \sqrt{2} } )}^{2} {( \cos( \frac{\pi}{11} ) + \sin( \frac{\pi}{11} ) )}^{2} } = \\ = {( \sqrt{2} )}^{2} = 2$