Câu hỏi của Trang Nana

Question

Cho biểu thức

$F\left(x\right)=sin\left(\frac{3\pi}{2}+x\right)+cos\left(\frac{27\pi}{2}-x\right)+sin\left(3\pi+x\right)-cos\left(7\pi-x\right)$

a) Rút...

Nguyễn Việt Lâm · Accepted Answer

$F\left(x\right)=sin\left(2\pi-\frac{\pi}{2}+x\right)+cos\left(14\pi-\frac{\pi}{2}-x\right)+sin\left(2x+\pi+x\right)-cos\left(6\pi+\pi-x\right)$

$=-sin\left(\frac{\pi}{2}-x\right)+cos\left(\frac{\pi}{2}+x\right)+sin\left(\pi+x\right)-cos\left(\pi-x\right)$

$=-cosx-sinx-sinx+cosx=-2sinx$

b/ $F\left(x\right)=-1\Leftrightarrow-2sinx=-1$

$\Rightarrow sinx=\frac{1}{2}\Rightarrow x=30^0$

Câu trả lời:

$F\left(x\right)=sin\left(2\pi-\frac{\pi}{2}+x\right)+cos\left(14\pi-\frac{\pi}{2}-x\right)+sin\left(2x+\pi+x\right)-cos\left(6\pi+\pi-x\right)$

$=-sin\left(\frac{\pi}{2}-x\right)+cos\left(\frac{\pi}{2}+x\right)+sin\left(\pi+x\right)-cos\left(\pi-x\right)$

$=-cosx-sinx-sinx+cosx=-2sinx$

b/ $F\left(x\right)=-1\Leftrightarrow-2sinx=-1$

$\Rightarrow sinx=\frac{1}{2}\Rightarrow x=30^0$