cho sin alpha+cos alpha=m. Tính: sin alpha-cos alpha 26/11/2021 Bởi Quinn cho sin alpha+cos alpha=m. Tính: sin alpha-cos alpha
$(sin\alpha+cos\alpha)^2= m^2$ $\Leftrightarrow sin^2\alpha + cos^2\alpha + 2sin\alpha.cos\alpha= m^2$ $\Leftrightarrow 2sin\alpha.cos\alpha = m^2-1$ $(sin\alpha – cos\alpha)^2= sin^2\alpha – 2sin\alpha.cos\alpha + cos^2\alpha$ $= 1-(m^2-1)= 2-m^2$ $\Leftrightarrow sin\alpha – cos\alpha= \sqrt{2-m^2}$ Bình luận
Đáp án: Theo đề bài : sin(a) + cos (a)=m [sin(a) + cos (a)]²=m² sin(a)²+cos(a)²+2.sin(a).cos(a)=m² 1 + 2sin(a).cos(a)=m² 2sin(a).cos(a)=m²-1 Ta có: sin(a)-cos(a)= [sin(a) – cos (a)]² =sin(a)²+cos(a)²-2.sin(a).cos(a) = 1 -(m²-1) = 2-m² => sin(a)-cos(a)=√2-m² Bình luận
$(sin\alpha+cos\alpha)^2= m^2$
$\Leftrightarrow sin^2\alpha + cos^2\alpha + 2sin\alpha.cos\alpha= m^2$
$\Leftrightarrow 2sin\alpha.cos\alpha = m^2-1$
$(sin\alpha – cos\alpha)^2= sin^2\alpha – 2sin\alpha.cos\alpha + cos^2\alpha$
$= 1-(m^2-1)= 2-m^2$
$\Leftrightarrow sin\alpha – cos\alpha= \sqrt{2-m^2}$
Đáp án:
Theo đề bài : sin(a) + cos (a)=m
[sin(a) + cos (a)]²=m²
sin(a)²+cos(a)²+2.sin(a).cos(a)=m²
1 + 2sin(a).cos(a)=m²
2sin(a).cos(a)=m²-1
Ta có: sin(a)-cos(a)= [sin(a) – cos (a)]²
=sin(a)²+cos(a)²-2.sin(a).cos(a)
= 1 -(m²-1)
= 2-m²
=> sin(a)-cos(a)=√2-m²