Question

28. Tổng các nghiệm của pt tan(2x -15°)=1 trên khoảng (-90°;90°) ?

34. Cho tan(x + π/2) -1=0 . Tính sin(2x -π/6)

Answer 1

28.

\(tan\left(2x-15^0\right)=1\Leftrightarrow2x-15^0=45^0+k180^0\)

\(\Leftrightarrow2x=60^0+k180^0\)

\(\Leftrightarrow x=30^0+k90^0\)

\(-90^0\le30^0+k90^0\le90^0\Rightarrow k=\left\{-1;0\right\}\)

\(\Rightarrow x=\left\{-60^0;30^0\right\}\Rightarrow\sum x=-30^0\)

34.

\(tan\left(x+\frac{\pi}{2}\right)=1\Leftrightarrow x+\frac{\pi}{2}=\frac{\pi}{4}+k\pi\)

\(\Rightarrow x=-\frac{\pi}{4}+k\pi\)

\(\Rightarrow sin\left(2x-\frac{\pi}{6}\right)=sin\left[2\left(-\frac{\pi}{4}+k\pi\right)-\frac{\pi}{6}\right]\)

\(=sin\left(-\frac{2\pi}{3}+k2\pi\right)=sin\left(-\frac{2\pi}{3}\right)=-\frac{\sqrt{3}}{2}\)