Question

cho biết \(\cos\alpha\)+\(\sin\)\(\alpha\)=m.Tính P=\(\left|\cos\alpha-\sin\alpha\right|\)theo m

Answer 1

\(cosa+sina=m\)

=>\(\left(cosa+sina\right)^2=m^2\)

=>\(1+2\cdot sina\cdot cosa=m^2\)

=>\(2\cdot sina\cdot cosa=m^2-1\)

\(P=\left|cosa-sina\right|\)

\(=\sqrt{\left(cosa-sina\right)^2}\)

\(=\sqrt{cos^2a+sin^2a-2cosa\cdot sina}\)

\(=\sqrt{1-\left(m^2-1\right)}=\sqrt{2-m^2}\)