Question

Rút gọn các biểu thức sau:

Answer 1

\(B=cos\left(\pi+\dfrac{\pi}{2}-a\right)-sin\left(8\pi-a\right)+tan\left(3\pi+\dfrac{\pi}{2}-a\right)+cot\left(3\pi-a\right)\)

\(=-cos\left(\dfrac{\pi}{2}-a\right)-sin\left(-a\right)+tan\left(\dfrac{\pi}{2}-a\right)+cot\left(-a\right)\)

\(=-sina+sina+cota-cota=0\)

\(C=sin\left(a+\dfrac{\pi}{2}+42\pi\right)-cos\left(2022\pi-a\right)+sin^2\left(33\pi+a\right)+sin^2\left(a-\dfrac{\pi}{2}-2\pi\right)\)

\(=sin\left(a+\dfrac{\pi}{2}\right)-cosa+sin^2a+sin^2\left(\dfrac{\pi}{2}-a\right)\)

\(=cosa-cosa+sin^2a+cos^2a=1\)