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Question

Rút gọn các biểu thức sau:

Nguyễn Việt Lâm · Accepted Answer

$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)$$=cosa-cosa+sin^2a+cos^2a=1$Câu trả lời: $B=cos\left(\pi+\dfrac{\pi}{2}-a\right)-sin\left(8\pi-a\right)+tan\left(3\pi+\dfrac{\pi}{2}-a\right)+cot\left(3\pi-a\right)$$=-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$

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