Rút gọn biểu thức
A = \(5\sin\left(\dfrac{11\pi}{2}-\alpha\right)+\cos\left(\dfrac{\pi}{2}+\alpha\right)-\sin\left(\alpha-\pi\right)\)
B= \(6\tan\left(2021\pi-\alpha\right)+\cos\left(\alpha+2022\pi\right)-\sin\alpha\)
C= \(\sin\left(\dfrac{17\pi}{2}-\alpha\right)+\cos\left(\alpha-\dfrac{\pi}{2}\right)\)
\(A=5sin\left(6\pi-\dfrac{\pi}{2}-a\right)+sin\left(\dfrac{\pi}{2}-\dfrac{\pi}{2}-a\right)+sin\left(\pi-a\right)\)
\(=-5sin\left(\dfrac{\pi}{2}+a\right)+sin\left(-a\right)+sina=-5cos\left(\dfrac{\pi}{2}-\dfrac{\pi}{2}-a\right)=-5cos\left(-a\right)=-5cosa\)
\(B=6tan\left(-a\right)+cosa-sina=-6tana+cosa-sina\)
\(C=sin\left(8\pi+\dfrac{\pi}{2}-a\right)+cos\left(\dfrac{\pi}{2}-a\right)=sin\left(\dfrac{\pi}{2}-a\right)+cos\left(\dfrac{\pi}{2}-a\right)=cosa+sina\)
