Question

  Rút gọn các biểu thức sau

Answer 1

\(a,A=cos\left(\alpha+\pi\right)+sin\left(\alpha+\dfrac{5\pi}{2}\right)-tan\left(\alpha+\dfrac{\pi}{2}\right).tan\left(\pi-\alpha\right)\)
\(=-cos\alpha+sin\left(\alpha+\dfrac{\pi}{2}+2\pi\right)+tan\left(\pi-\alpha-\dfrac{\pi}{2}\right).-tan\alpha\)
\(=-cos\alpha+sin\left(\alpha+\dfrac{\pi}{2}\right)+tan\left(\dfrac{\pi}{2}-\alpha\right).-tan\alpha\)
\(=-cos\alpha+sin\left(\pi-\alpha-\dfrac{\pi}{2}\right)+cot\alpha.-tan\alpha\)
\(=-cos\alpha+cos\alpha-1\)
\(=0-1=-1\)
 

Answer 2

\(b,B=cos\left(\dfrac{\pi}{2}-\alpha\right).sin\left(\beta+\pi\right)-sin\left(2\pi-\alpha\right).cos\left(\beta-\dfrac{\pi}{2}\right)\)
\(=sin\alpha.-sin\beta-sin\left(-\alpha\right).sin\left(\dfrac{\pi}{2}-\beta+\dfrac{\pi}{2}\right)\)
\(=-sin\alpha.sin\beta-\left(-sin\alpha\right).sin\left(\pi-\beta\right)\)
\(=-sin\alpha.sin\beta+sin\alpha.sin\beta\)
\(=0\)