Question

Chứng minh : \(cos\left(\alpha-\dfrac{\pi}{2}\right)=sin\alpha\)

Answer 1

\(cos\left(\alpha-\dfrac{\pi}{2}\right)=sin\alpha\)

\(\Leftrightarrow cos\left(\alpha-\dfrac{\pi}{2}\right)=cos\left(\dfrac{\pi}{2}-\alpha\right)\)

\(\Leftrightarrow\alpha\in R\)

Answer 2

    \(cos\left(\alpha-\dfrac{\pi}{2}\right)=cos\alpha\cdot cos\dfrac{\pi}{2}+sin\alpha\cdot sin\dfrac{\pi}{2}\)

\(=cos\alpha\cdot0+sin\alpha\cdot1=sin\alpha\)

\(\Rightarrow\) Đẳng thức được chứng minh.