Question

[Lê Đức Hoàng]

mn giup e mấy câu này vs T_T

1. sin(\(\frac{\pi}{3}\)-x), biết cosx= \(-\frac{12}{13}\) (\(\frac{\pi}{2}< \frac{x}{2}< \frac{3\pi}{4}\))

2.cot\(\left(x-\frac{\pi}{4}\right)\), biết \(sinx=\frac{-4}{5}\left(\pi< x< \frac{3\pi}{2}\right)\)

3.tan\(\left(x+\frac{\pi}{4}\right)\), biết \(cot\left(\frac{5\pi}{2}-x\right)=2\)

Answer 1

[Nguyễn Việt Lâm]

a/ \(\pi< x< \frac{3\pi}{2}\Rightarrow sinx< 0\)

\(\Rightarrow sinx=-\sqrt{1-cos^2x}=-\frac{5}{13}\)

\(sin\left(\frac{\pi}{3}-x\right)=sin\frac{\pi}{3}cosx-cos\frac{\pi}{3}sinx=\frac{\sqrt{3}}{2}.\left(-\frac{12}{13}\right)-\frac{1}{2}.\left(-\frac{5}{13}\right)=\frac{5-12\sqrt{3}}{26}\)

b/ \(\pi< x< \frac{3\pi}{2}\Rightarrow cosx< 0\)

\(\Rightarrow cosx=-\sqrt{1-sin^2x}=-\frac{3}{5}\)

\(cot\left(x-\frac{\pi}{4}\right)=\frac{cos\left(x-\frac{\pi}{4}\right)}{sin\left(x-\frac{\pi}{4}\right)}=\frac{sinx+cosx}{sinx-cosx}=7\)

c/ \(cot\left(\frac{5\pi}{2}-x\right)=cot\left(2\pi+\frac{\pi}{2}-x\right)=tanx=2\)

\(\Rightarrow tan\left(x+\frac{\pi}{4}\right)=\frac{tanx+tan\frac{\pi}{4}}{1-tanx.tan\frac{\pi}{4}}=\frac{2+1}{1-2.1}=-3\)

Answer 2

[Lê Đức Hoàng]

tính giá tri biểu thức ạ e quên chưa ghi