Question

СРОЧНО
Найти значение выражения:

cos(pi/4-B)-cos(pi/4-B) если sin B = 1

Answer 1

$sin\beta=1\\\\\\cos(\frac{\pi}{4}-\beta)-cos(\frac{\pi}{4}+\beta)=\\\\=cos\frac{\pi}{4}\;cos\beta+sin\frac{\pi}{4}\;sin\beta-(cos\frac{\pi}{4}\;cos\beta-sin\frac{\pi}{4}\;sin\beta)=\\\\=\frac{\sqrt{2}*cos\beta}{2}+\frac{\sqrt{2}*sin\beta}{2}-\frac{\sqrt{2}*cos\beta}{2}+\frac{\sqrt{2}*sin\beta}{2}=\\\\=\frac{\sqrt{2}*cos\beta+\sqrt{2}*sin\beta-\sqrt{2}*cos\beta+\sqrt{2}*sin\beta}{2}=\\\\=\frac{2\sqrt{2}*sin\beta}{2}=\sqrt{2}*sin\beta=\sqrt{2}*1=\boxed{\sqrt{2}}$