Question

Diễn tả giá trị lượng giác của góc sau bằng giá trị lượng giác của góc x 

\(cos^{2015}\left(x-\dfrac{11\pi}{2}\right);cos^{2019}\left(x+\dfrac{7\pi}{2}\right);sin^{2019}\left(\dfrac{5\pi}{2}-x\right);cot^2\left(x-\dfrac{\pi}{2}\right)\)

Answer 1

\(cos^{2015}\left(x-\frac{11\pi}{2}\right)\)

\(=cos^{2015}\left(x+\frac{\pi}{2}-\frac{12\pi}{2}\right)=cos^{2015}\left(x+\frac{\pi}{2}-6\pi\right)\)

\(=cos^{2015}\left(x+\frac{\pi}{2}\right)=-\sin^{2015}x\)

\(cos^{2019}\left(x+\frac{7\pi}{2}\right)\)

\(=cos^{2019}\left(x-\frac{\pi}{2}+4\pi\right)=cos^{2019}\left(x-\frac{\pi}{2}\right)\)

\(=cos^{2019}\left(\frac{\pi}{2}-x\right)=\sin^{2019}x\)

\(\sin^{2019}\left(\frac52\pi-x\right)=\sin^{2019}\left(2\pi+\frac{\pi}{2}-x\right)\)

\(=\sin^{2019}\left(\frac{\pi}{2}-x\right)=cos^{2019}x\)

\(\cot^2\left(x-\frac{\pi}{2}\right)=\frac{1}{\sin^2\left(x-\frac{\pi}{2}\right)}-1=\frac{1}{\sin^2\left(\frac{\pi}{2}-x\right)}-1=\frac{1}{cos^2x}-1\)

\(=\tan^2x\)