Question

Найти cosa если sina=(корень из 2)-1

Answer 1

cos²a+sin²a=1
cos²a=1-sin²a
откуда
$cos \alpha = \sqrt{1 - { \sin \:^{2} ( \alpha ) \: } } = \\ = \sqrt{1 - ( \sqrt{2} - 1) ^{2} } = \\ = \sqrt{1 - (2 - 2 \sqrt{2} + 1) } = \\ = \sqrt{2 \sqrt{2 } - 2 } = \sqrt{2} \sqrt{ \sqrt{2 } - 1}$
или
$cos \alpha = - \sqrt{1 - { \sin \:^{2} ( \alpha ) \: } } = \\ = - \sqrt{1 - ( \sqrt{2} - 1) ^{2} } = \\ = - \sqrt{1 - (2 - 2 \sqrt{2} + 1) } = \\ = - \sqrt{2 \sqrt{2 } - 2 } = - \sqrt{2} \sqrt{ \sqrt{2 } - 1}$